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LIBRARY 


UNIVERSITY  OF  CALIFORNIA. 

%eceiveii         ....y'Wy'^^       ,  i8g2 - 

Accessions  No.  4^ J ^3^  ■  Class  No. 


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U.  S.  MILITARY  ACAOeivlV. 


COURSE  OF  INSTRUCTION 


IN 


ORDNANCE  AND  GUNNERY 


TEXT. 


BY- 


Captain   HENRY    METCALFE, 

Ordnance  Dep't,  U.  S.  Army, 

Instructor  of  Ordnance  and  G winery,  U.  S.  Military  Academy. 


SKCOND   KDITION. 


^^  OP  TEra"^^ 

UHiyERSITY] 

*^^^       —        1891. 


Copyright,  1891, 

BY 

Henry  Metcalfe. 


CONTENTS 


CHAPTER 

I. 

CHAPTER 

II. 

CHAPTER 

III. 

CHAPTER 

IV. 

CHAPTER 

V. 

CHAPTER 

VI.- 

CHAPTER 

VII.- 

CHAPTER 

VIII. 

CHAPTER 

IX.- 

CHAPTER 

X. 

CHAPTER 

XI.- 

CHAPTER 

XII.- 

CHAPTER 

XIII.- 

CHAPTER 

XIV.- 

CHAPTER 

XV. 

CHAPTER 

XVI.- 

CHAPTER 

XVII.- 

CHAPTER 

XVIIL- 

CHAPTER 

XIX.- 

CHAPTER 

XX.- 

CHAPTER 

XXI.- 

CHAPTER 

XXII.- 

CHAPTER 

XXIII.- 

CHAPTER 

XXIV.- 

CHAPTER 

XXV.- 

CHAPTER 

XXVI.- 

CHAPTER 

XXVII.- 

CHAPTER  : 

XXVIII.- 

CHAPTER 

XXIX.- 

CHAPTER 

XXX.- 

-Definitions.  ) 

-Explosive  Agents. 

-Ingredients  of  Gunpowder.      , 

-Manufacture  of  Gunpowder.  J 

-Interior  Ballistics. 

-Velocimeters. 

-Pressure  Gauges. 

-Phenomena  of  Conversion. 

-Noble  and  Abel's  Experiments. 

-Combustion  of  Gunpowder  in  the  Air. 

-Combustion  of  Gunpowder  in  the  Gun. 

-Sarrau's  Formula  for  Interior  Ballistics. 

-History  of  Gunpowder. 

-High  Explosives.  -  / 

-Metallurgy. 

-Projectiles  and  Armor. 

-Manufacture  of  Projectiles. 

-Means  of  Communicating  Fire. 

-Gun  Construction. 

-Exterior  Ballistics. 

-Varieties  of  Cannon. 

-Artillery  Carriages,  Principles. 

-Various  Artillery  Carriages. 

-Horse  and  Harness. 

-Artillery  Machines. 

-Hand  Arms.  -  { 

-Small  Arm  Ammunition. 

-Small  Arms.  '- 1 

-Cannon  Without  Recoil. 

-Accuracy  of  Fire. 


PREFACE  TO  SECOND  EDITION, 


The  great  advances  which  have  been  recently  made  in  our 
knowledge  of  the  properties  of  gunpowder  have  subjugated 
the  "  Spirit  of  Artillery,"  as  this  agent  has  been  termed,  to  a 
seemingly  docile  servitude.  These,  with  corresponding 
improvements  in  Metallurgy,  have  led  to  such  changes  in 
nearly  all  that  relates  to  fire-arms  as  to  make  necessary 
a  comprehensive  revision  of  the  course  of  Ordnance  and 
Gunnery,  established  by  the  late  Colonel  James  G.  Benton 
in  1861,  and  modified  from  time  to  time  by  his  successors  on 
the  Academic  Board. 

The  subject  has  outgrown  the  limits  of  the  small  encyclo- 
pedia in  which  Benton  comprised  all  that  was  then  essential 
for  the  ordinary  officer,  as  well  as  for  the  student,  to  know  of 
the  materiel  of  war. 

It  has  also  lost  much  of  the  stability  which  characterized 
it  when  spherical  projectiles  were  still  generally  employed. 
The  labors  of  men  of  science  and  the  energy  of  inventors 
are  continually  extending  the  boundaries  of  knowledge  and 
undermining  positions  which  appear  most  fixed. 

Therefore,  instead  of  giving  to  the  course  a  descriptiv^e 
character,  it  appears  advisable  to  frame  it  so  as  to  present 
as  simply  as  possible  such  of  its  principles  as  are  the  most 
important,  and  appear  the  best  established. 

By  employing  the  short  time  available  for  this  course  in 
teaching  such  principles,  the  student,  although  less  familar 
with  existing  forms  and  methods  than  after  the  study  of  the 
former  course,  may  possibly  be  better  fitted  to  understand 
the  causes  of  changes  in  materiel  which  are  now  so  frequent, 
and,  as  his  experience  increases,  to  wisely  advise  the  direc- 
tion that  such  changes  should  take. 


VI  PREFACE. 


The  selection,  enunciation  and  deduction  of  such  princi- 
ples in  a  suitable  form  is  rather  embarrassed  than  assisted 
by  the  mass  of  specialized  knowledge  to  be  found  in  the 
Government  reports  and  in  the  periodical  press.  In  fact, 
had  it  not  been  for  the  admirable  text-books  used  at  the 
^'''Ecole  d'' Application  de  VArtillerie  et  du  Genie^''  at  Fontaine- 
bleau,  France,  for  a  set  of  which  the  author  is  obliged  to 
superior  military  and  diplomatic  authority,  it  would  not 
have  been  possible  for  him  to  prepare  many  of  the  following 
pages. 

Graphical  methods  have  been  freely  used,  both  to  express 
abstract  relations  and  to  avoid  description.  In  order  to 
reheve  the  memory  and  to  train  the  student  in  reading 
mechanical  drawings,  it  is  intended  that  the  more  elaborate 
shall  be  recited  on  from  the  book. 

It  has  been  attempted  to  give  the  antecedents  of  present 
forms,  briefly,  but  so  as  to  indicate  the  general  lines  fol- 
lowed in  their  evolution  and  possibly  to  anticipate  the 
direction  in  which  their  improvement  tends.  In  so  doing 
more  stress  than  heretofore  has  been  laid  upon  the  practice 
of  the  workshops;  since  the  history  of  invention  shows 
that  this  has  had  as  much  to  do  with  the  march  of  improve- 
ment as  a  special  knowledge  of  the  military  necessities  of 
any  particular  case. 

The  thanks  of  the  author  are  due  : 

To  Mr.  Geo.  H.  Chase,  of  the  Midvale  Steel  Works,  Phila- 
delphia, for  revising  Chapter  XV. 

To  Captain  Z.  L.  Bruff,  Ordnance  Department,  for  the 
appendix  to  Chapter  XIX,  relating  to  the  Elastic  Strength 
of  Guns. 

To  Private  C.  August  Schopper,  of  his  detachment,  for 
most  of  the  drawings  used  in  illustration. 

West  Point,  New  York,  yuly  1,  1891. 

HENRY  METCALFE, 


Bibliography  of  the  Principal  Works  Consulted. 


Benton's  Ordnance  and  Gunnery.     6th  Edition. 

Mordecai's  Revision  of  Benton.     Pamphlets,  U.  S.  M.  A. 

McKinlay's  Text-Book  of  Gunnery.     British.     1887. 

Cooke's  Naval  Ordnance  and  Gunnery.     2nd  Edition. 

Text  Book  of  Ordnance  and  Gunnery,  U.  S.  N,  A.     1887 

Noble  and  Abel's  Experiments  on  Fired  Gunpowder.     2  Vols,     1880. 

Proceedings  U.  S.  Naval  Insiitute.     Current  series. 

Encyclopedia  Brittanica.     9th  Edition. 

Bloxam's  Chemistry.     6th  Edition. 

Byrne's  Metal  Worker's  Assistant.     1869. 

Goodeve's  Principles  of  Mechanism.     1876. 

Reports  of  the  Chief  of  Ordnance,  U.  S,  A.     1872 — 1890. 

Ordnance  Notes,  U.  S.  A. 

Notes  on  the  Construction  of  Ordnance,  U.  S.  A.     Current  series. 

Reports  on  Naval  Progress,  U.  S.  N.     1887 — 1890. 

Principal  French  Works. 
Roulin's.     Poudres  de  Guerre  et  Balistique  Int^rieure.     1884. 

do  Armes  Portatives.     1885. 

Pi^bourg.     Fabrication  de  la  Poudre.     1884. 

do  Pyrotechnic.     1884. 

Jouffret.     Les  Projectiles.     1881. 
Berthelot.     Sur  la  force  de  la  Poudre.     1872. 
Muzeau.     Effets  du  tir  sur  les  affuts.     1884. 
Bornecque.     Armes  ^  repetition.     1888. 
Malengrau.     L'Artillerie  a  I'Exposition.     1890. 
Aide  Memoire.     Artillerie.     1887. 

Referritig  to  Chapter  XII. 
Meig's  and  Ingersoll's  Interior  Ballistics,  U.  S.  N.  A.  1887. 
Medcalfe and  Howard.  Notes  on  Construction  of  Ordnance.  N0S.36&42. 
The  above  are  derived  principally  from  Sarrau's  **  Researches  on  the 
Effect  of  Powder,"  translated  in  the  Proceedings  of  the  U.  S.  Naval 
Institute.  Vol.  X.  Whole  No.  28.  And  from  **  Researches  on  the 
Loading  of  Fire  Arms."     1882. 


VIU    BIBLIOGRAPHY  OF  THE  PRINCIPAL  WORKS  CoNStJLtED. 


Referring  to  Chapter  XIV. 
Abbott's  Submarine  Mines.     i88i.     Appendices. 
Eissler's  High  Explosives.     1884. 
Monroe's  Notes  on  Explosives.     1888. 

Referring  to  Chapter  XV. 
Greenwood's  Steel  and  Iron.     1884. 
Bauerman's  Metallurgy  of  Iron.     1868. 
Jean's  Steel,  History,  Manufacture,  etc.     1880. 
Thurston's  Text-Book  of  Materials  of  Construction.     1886. 
Chernoff  on  the  Structure  of  Steel.     Note  on  Construction  of  Ordnance. 

No.  22. 
Brinell  on  the  Structure  of  Steel.    Note  on  the  Construction  of  Ordnance. 

No.  37. 

Referring  to  Chapter  XVI. 
Proceedings  U.  S.  Naval  Institute.     No.  56.     1890. 
Ordnance  Construction  Notes,  28,  49. 

Referring  to  Chapter  XVII. 
Ordnance  Construction  Note,  26. 

Refe'^ring  to  Chapter  XIX. 
Ordnance  Construction  Notes,  9,  19. 

Referring  to  Chapter  XX. 
Bruff 's  Ballistics.     1885. 
Ingalls'  Exterior  Ballistics.     1886. 

Referring  to  Chapter  XXX. 
Glennon's  Accuracy  and  Probability  of  Fire.     1888. 


REMARK.  —  The  unusual  method  of  paging  adopted  in  this  work  is 
intended  to  facilitate  its  revision,  since  new  chapters  can  be  inserted  with- 
out disturbing  the  sequence  of  the  following  pages. 


INDEX 


The  heavy  figures  refer  to  the  number  of  the  chapter,  and  the  lighter 
figures  to  that  of  the  page. 


Abbott's  experiments,  14, 1. 

Abbreviations,  1,  4. 

Abel,  gun  cotton,  14,  10. 

Absolute  error,  30,  '24;  force  of 

gunpowder,  9,  6. 

Accidents,  fuzes,  18,  19; gunpow- 
der,  4,  1;   high   explosives, 

14,  1. 

Accles  feed,  29,  6. 

Accuracy  of  lire,  30,  5; estimated, 

30,  23,  35. 

Acoustic  telemeters,  30,  11. 

Air,  combustion  in,  8,  2,  10,  3,  4,  12, 
3; packing,  7,  4,  21 ,  7; re- 
sistance of,  16,  1,  20,  8;  spac- 
ing, 11,  14;  trajectory  in,  20, 

18. 

Aluminium  in  steel,  15,  20. 

Ammonium  nitrate,  3,  7. 

Ammunition  and  arms,  relation,  27, 
1; chest,  22, 28; rapid  fire, 

29,  18,  20;  small  arm,  27,  9, 

28,  19; supply  of,  2S,  17. 

Ancient  cannon,  13, 1; carriages, 

i8l,  20; gunpowder,  13,  2. 

Analysis  of  gunpowder,  2,  10,  9,  2, 
11,  29. 

Angle  of  fall,  20,  37,  30,  35;  of 

draught,  24,  3. 

Animal  power,  24,  1,  3,  28,  2. 

Animate  objects,  10,  23; areas, 

30,  48. 

Annapolis  armor  tests,  16,  43. 

Annealability,  15,  23. 

Annealing,  15, 38, 51, 52, 57; vrater, 

15,54. 
Anvils,   forging,   15,  44.  46;  for 

])rimers,  27,  4. 


Armor,  kinds  of,  16,  36; piercing 

shell,  16, 20, 29, 21; penetration 

of,  16,  36; test  for  projectiles, 

17.  18. 

Arms  and  ammunition,  relation,  27, 1. 

Artillery  carriages,  22, 1; system 

of,  a  1,3. 

Assembling  cannon,  16,  58. 

Axle,  22,  24. 

B. 

Back  gear,  17, 12. 

Backing,  armor,  16,  37. 

Back  rest,  17, 13. 

IJallistics,  interior,  5,  1; exterior, 

20, 1; coefficient  (gunpowder) 

12,  13,  28.  21; projectile, 

16,  2,  20,  11,  23; formulae,  20, 

28,  47; tables,  20,  27.  53. 

Balloting  of  projectile,  16,  15. 

Bands,  carrying,  4,  5;  rotating, 

16,  12,  15,  17,2,15. 

Barbette  carriage,  22,  2,  23,  5. 

Harlow's  law,  19,  J,  4. 

Barrels,  mixing,  4,  5; tumbling, 

4,  4; small  arm,  28,  2. 

Bashforth,  experiments,    20,  9;  

target,  6, 15 

Basic  process.  15,  19,  35,  37. 

Batteries,  electric,  6, 15,  18,  5. 

Bayonet,  26, 1. 

Beaten  zone,  30,  49. 

Belleville  springs,  22,  19,  23,  4. 

Bellite,  14,  16. 

Belts,  17,  12. 

Benton  velocimeter,  6,  3. 

Berdan  telemeter,  30, 15; primer, 

27,4. 

Berihelot's  theory,  explosives,  2,  3. 

Bessemer   process,    15,  32,  35  j   »»« 


ind:  X. 


Bickford  fuze,  18,  2. 

Blacking  arms,  aS,  29. 

lilack  wash,  l"?,  3. 

Blasts,  size  of,  14,  2. 

Blasting  fuze,  18,  2; powder,  8, 

7,  9,  9,  2. 
Blending  gunpowder,  4, 13. 
Blister  steel,  15, 14,  30. 
Blooms,  15,  43. 
Blow  holes,  15,  21. 
l?o]t  guns,  88,  a. 
Bomford's  experiment,  7,  15. 

Bore,  rocket,  16, 44; and  parts  1, 1. 

Boring,  17,  13. 

Bormann  fuze,  18,  9. 

Boxer  shrapnel,  16,  31,  32. 

Box  magazines,  88,  11. 

Brakes,  22,  11,  18. 

Brinell's  experiments,  15,  49. 

Brgger's  chronograph,  6,  10. 

Breaching,  14,  19,  16,  20. 

Breech,  1,  2. 

Breeching,  24,  7. 

Breech  loading,  advantages  of,  II,  16, 

13,  2,  28,  1; projectiles, 

5,  3,   16, 14; small  arms, 

28,5. 
Broad  well  ring,  21,  7. 
Bronze,   15,  14,  20,  24,   19,  12;    

quenched,  15,  22. 
Browning  arms,  28,  29. 
Blown  powder.    (  See  Cocoa.) 
Bruce  feed,  29,  5. 
Brug^re  powder,  1 4, 18. 
Buffers,  23, 14. 
Buffington  brake,  22,  19,  23,  2;  

carriage,  23,  1. 
Built  up  guns,  19,  12,22. 
Bullet,  manufacture,  27,  8; small 

caliber,  28,  2,  20. 
Burden  of  ammunition,  28,  4,  28,  18 
Bursting  charges,  14,  7,  19,  16,  20,  26, 

32,  19,  17,  29, 17. 
Butler  projectile,  16, 13. 
Buttofrifle,  28,  3. 


C. 


Caisson,  22,  29,  23,  2. 
Cake  powder,  13,  i, 


Caking,  16,  20. 

Caliber,  1,  1; influence  of,  16,  7, 

17; small  arm,  28,  2. 

Canet  system,  21, 13. 

Canister,  16,  23,  25,  28,  82,  28. 

Cannelures,  27,  8. 

Cannon,  1,  1; B.  L.,  5,  3,  13,  2; 

construction  of,  19, 1,  22; 

dimensions  of,  13,  25,  21,  22; 

disabling,  14,  20; metals,  15, 

13,  24;  M.  L  ,  6,  3,  13,  2,  21, 

4;  nomenclature,   1,  1;  

proportions  of,  5,  2,  19,  46; 

varieties  of,  21, 1. 

Carbine,  28, 1. 

Carbo-hydrates,  11,  28. 

Carbon,  cement,  15, 18,  48; hard- 
ening, 15, 18,  48; states  of,  15, 

48; in  steel,  15,  18. 

Carbonizers,  15,  28,  32,  36. 

Carcass,  16,  22. 

Carriages,  artillery,  22, 1. 

Cartridge,  anvil,  27,  4,  5;  cor- 
roded, 27,  6; limit  of  size,  29, 

IS; manufacture  of,  27,  6; 

metals,  27,  5; origin,  87,  1; 

resizing,  27,  6, 

Case  hardening,  15,  27. 

Case  shot,  16,  18,  23. 

Castan's  powder,  4, 12. 

Casting,  17, 1; cannon,  15, 58,  19, 

12; ingots,  15,  33,  56; steel, 

15,  42. 

Cast  iron,  15,  24; projectiles, 

16,  5,  6. 

Cavity  in  shells,  16, 18,  22. 

Cellular  theory,  15,  21. 

Cement  carbon,  15,  18,  48. 

Center  of  impact,  30,  23;  marks, 

17, 13. 

Centering  projectile,  16,  12. 

Central  fire  cartridge,  27,  4. 

Chamber,  1,  1,  5,  3. 

Change  gear,  17, 12. 

Charcoal,  brown,  3,  5,  4,  14,  11,  28  ; 
material,  etc.,  3,  1;  pre- 
paration,   3,  2;  properties,  3, 

4;  — spontaneous  ignition,  3,  4. 

Cbase,  1,  3r 


INDEX. 


Chassis,  32,  2. 

Chauvenet's  table,  30,  36. 

Chest,  ammunition,  32,  28. 

Chi  (x),  coefficient,  11, 20, 13, 28; 

factors  of,   13,  29; maximum 

value  of,  13,  31. 
Chilled  iron,  16,  5,  17,  6,  9, 14. 
Chlorates,  3,  7,  14,  19. 
Choice  of  formulae,  Sarrau,  13,  6. 
Chromium  in  steel,  15,  20. 
Chronograph,  Le  Bouleng6,  6, 6. 
Chronoscope,  6, 13. 
Chuck,  lathe,  17, 13. 
Clips,  33,  9,  33,  6 
Cluster,  16,  23. 
Cocoa  powder,  manufacture,  4,  13 ; 

theory,  11,  27. 

Coefficient,  ballistic,  13,  13,  16,  •?,  30, 

11,  23  ;  of  efficiency,  30,  52  ; 

of  elasticity,  16,  4,  10,  19,9, 

22;  internal  ballistic,  various, 

11, 19;  Wertheims,  19, 2,  3,  25. 

Cold  and  heat,  on  high   explosives, 

14,  6;  rolling,  15,  24,  42;  

shuts,  15,44. 
Collective  fire,  30,  48. 
Combination  fuze,  18,  6, 15. 
Combustion,  condition  of,  3,  4; in 

air,  8,  2,  10,  1;  in  gun,  8,  2, 

11,  1,  4;  rates,  8,  2,  JO,  3,  13, 

3; volume,  11, 1. 

Commercial  values,  3,  9,  14,  2,  31,  fi. 
Common  properties,  high  explosives, 

14,2. 
Communicating  fire,  18, 1. 
Component  parts  of  arms,  38,  2;  

of  ammunition,  37,  8. 
Composition  of  gunpowder,  3,  10,  9,  2. 
Compound  cylinder,  strength  of,  19, 

14,  33. 
Compressive  projectiles,  5,  3,  16, 14. 
Concrete  powder,  4.  11. 
Concussion  fuze,  18, 11. 
Condie's  hammer,  15,  46. 
Conditions  of  loading,  13,  16. 
Cone  of  dispersion,  16,  23,  26,  30,  49; 

pulley,  17, 11. 

Constants,  physical,  34,  2,  38, 16;  


Constitution  of  steel,  15, 16. 
Converted  guns,  II,  21,  19,  8,  31,  3, 

5,  38, 15, 
Conversion  of  gunpowder,  3,  1;  

rate  of  8,  3,  10,  2,  13,  3; phe- 
nomena of,  8, 1. 
Cooling,  15,  21,  49. 
Cope,  17,  5. 
Cores,  17,  4,  8, 11. 
Coring,  15,  56. 
Corning  mill,  4,  11,  13.  3. 
Counter  recoil,  33,  18;  shaft,  17, 

12 
Cradle,  35,  2. 
Cranes,  1 5,  33, 

Crank  axle,  33, 29; kinds  of,  39, 7. 

Crozier's  deduction,  19,  27; gun, 

19,  18. 
Crucible  steel,  15,  31. 
Crusher  gauge,  7,  4. 
Crystallization,  15,  21. 
Cube,  elastic,  equilibrium,  19,  25. 
Cubic  law,  30,  12,  16. 
Cup-anvil,  37,  4. 
Cupola  furnace,  15, 25. 
Curvature  of  cutting  arms,  36,  3. 

Cutting  arms,  36,  2; speed,  17, 12. 

Cut-ofl",  38,  11.  * 

Cylinder,  elastic,  equilibrium,  19,  26, 

31; gauge,  17, 17; strength 

of,  16,  19,  19,  6,  31,  33. 


Damascus  steel,  15,  55. 

Dangerous    fragment,    16,    19 ;    

space,    1,  3,    30,  39,  43,  49,  38,  4  ; 

zone,  30,  49. 

Dank's  furnace,  15,  29. 

De  Bange  gas  check,  31,  8. 

Definitions,  general,  1,  1. 

Deformation,  process  of,  7,  3. 

Delayed  action  fuze,  18,  19. 

De  Marre,  formula  for  armor,  16,40. 

Demolition,  14,  19. 

Density,    gravimetric,   9,  3 ;    of 

loading,  9,  4,  12,  11,  14,  13,  1; 

sectional,  16,1; — spherical,  16,6. 
Departure,   angle   of,   30,  2,   45j  -i— ™» 

liue  Of,  20, 1, 


INDEX. 


Depression  range  finder,  30, 14. 

DesignoUe  powder,  1*,  17. 

Detachable  magazine,  38,  11. 

Detonation,  2,  3,  4, 14,  3;  sympa- 
thetic, 8,  5. 

Detonator,  3,  5,  14, 3,  18, 3;  tube, 

18,2. 

Development  of  small  arms,  28,  17. 

Deviations,  80, 4,  30, 6, 23; causes 

of,  30,  6. 

Dimensions  of  cannon,  changes  in, 
19,  27,  37. 

Dirigibility,  29,  13. 

Disabling  cannon,  14,  20. 

Disappearing  carriage,  83,  13. 

Dish  of  wheel,  23,  24. 

Disjunctor,  6,  4,  7. 

Dispart,  1,  2. 

Dissociation,  3, 1. 

Distance,  estimation  of,  30, 10.     , 

Drag,  17,  5. 

Draught,  angle  of,  34,  3; horse, 

34, 1; of  patterns,  17,  4. 

Drawn  cartridge,  37,  7. 

Drift,  30,  4,  30,  8. 

Drill  cartridge,  39,  20. 

Drop  test,  15, 15. 

Drying  gunpowder,  4, 12. 

Dog,  lathe,  ir,  13. 

Ductility,  15, 11. 

Dusting  gunpowder,  4,  13. 

Dynamite,  14,  4, 13. 


E. 

Early  cannon,  13,  1;  carriages, 

31,  20; shrapnel,  16,  30;  

fuzes,  18,  7,  8. 
Eccentric  turning,  38,  29. 
Economy,  coefficient  of,  11, 19. 
Effective  work  of  gunpowder,  11, 11. 
Effect,  factor  of,  11,  11,  21. 
Efficiency  of  fire,  30,  52. 
Elasticity,  15,  3, 11; coefficient  of, 

15,  4,  19,  22; varying,  19,  9. 

Elastic  limit,  15,  4,  19,  22; choice 

of,  19,  33;  gtrength  of  guns. 


Electric  batteries,  6,  15,  18,  5;  

primers,  18,  4. 

Electro-welding,  15,  23,  17, 15,  19,  19. 

Elevation,  angle  of,  30,  1. 

Emergency  powder,  8,  4. 

Emmensite,  14,  17. 

Energy,  3,  6,  5, 1,  16, 1, 18,  30,  22; 

of  recoil,  19,  19,  33,  4,  38, 16,  39, 

1; of  rotation,  16, 3; waste 

of,  9, 10,  11,  8. 

Engelhardt  buffer,  33, 18. 

Envelope  of  cluster,  16,  23; of  tra- 
jectory, 30,  6. 

Equilibrium,  equations  of,  19,  25,  27. 

Erosion  of  gun,  9, 13,  19,  20. 

Errors,  30,  6,  22,  24. 

Estimation  of  distances,  30, 10. 

Eta  iv),  11, 19. 

Eureka  projectile,  16, 14. 

Eprouvette,  7,  2,  9,  5,  13,  3. 

Expanding  projectile,  16, 13. 

Expansion  volume,  11,1; volumes 

of,  11, 12. 

Experiments,  rule  for,  9, 1. 

Exterior  ballistics,  definitions,  30,  1. 

Explosion,  5i,  1; orders  of,  3,  2,  4; 

Berthelot's  theory,  3,  3; 

temperature  of,  9,  8. 

Explosive    compounds,    J8,   10;    

gelatine,  14,  15;  high,  3,   10, 

14, 1; military,  3,  9; mix- 
tures, a,  9; reactions,  3,  3;  ^— 

strength  of,  2,  6; value  of, »,  8. 

Eye,  error  of,  30,  7. 


F. 

Face  plate,  1 7, 11. 

Facings,  17,  3. 

Factor  of  effect,  11, 11,  21. 

Fall,  angle  of,  30,  37,  30,  35. 

Feed  case,  39,  5 ;   of  machine 

guns,  39,  5, 12;  screw,  17,  12. 

Fermeture,  cannon,  31, 9, 15; small 

arms,  38,  5. 
Ferreous  metals,  15, 13,  24. 
Ferro-manganese,  15,  28j  ^UiQOn, 

15,28, 


INDEX. 


Field  cannon  B   L.,  21,  17; 

M.  L.,  81,  4;  mortar,  31,  17; 

sight,  30,  3, 

Final  velocity,  20, 17. 

Finishing  projectiles,  17,10. 

Fire,  angle  of,  20,  5,  22,  9; arms, 

1,  1;  classification  of,  20,  5; 

line  of,  20,  5;  plane  of, 

20,  4;  works,  14,  1<J. 

Firing,  2,  2;   gunpowder,  8,  1; 

high  explosives,  14,  3. 

Fiske  range  finder,  30,  15. 

Fixed  carbon,  16,  48;  magazines, 

28, 12. 
Flagler  fuze,  18, 17. 
Flasks,  17,  5,  8,  22,  3. 
Flatness  of  trajectory,    1,  3,  20,  23, 

40,  28,  20. 
Flow  of  metals,  15, 11,  87,  7. 
Folded  head,  27,3. 
Follow-board,  17,  5. 
Food  and  feed  of  arms,  27,  1,  29, 12. 
Force,  2,  7,  9,  7,  11,  2!),  12,  29,  14,  5. 
Forcite,  14,  14. 
Forging,  15,  45,  53;  cannon,  16, 

56; press,  16,  47. 

Fork,  establishing,  30,  21. 

Form  of  cannon,  6,  2,  9,  13,  13,  2,  19, 

6,  46,  21,  1. 
Founding,  17, 1. 
Fractures,  15,  20,  49. 
Free  carbon,  15,  48. 
French  fuze,  18,  13,  16;  system, 

21 ,  10. 

Freyi-e  gas  check,  21,  7. 

Friction    checks,  22,  11;  clutch, 

22,  12; .primers,  18,  3. 

Fioloir,  formula  for  armor,  16,  38. 
Fulminates,  2,  10,  14, 18. 
Fulmi-bran,  14,  11. 

Functions,  ballistic,  20, 27; experi- 
mental, 9,  1,  5;  independence 

of,  9,  1,  16,  34, 18, 16,  19,  16,  21,  2, 
19,  22,  22,  23,  24,  6,  26,  3,  4,  27,  4, 
28,  4,  15,  29,  4,  8,  15,  24. 

Fundamental  laws,  gun  construction, 
19,  29. 

Furnaces,  15,  25,  29,  39,  45. 

Fusibility,  15,  22. 

Fusse,  principles  of,  16,  J8, 28,  la,  7. 


Gadolin's  law,  19,  9,  20,44. 

Gardner  gun,  29,  7. 

Gaseous  fuel,  16,  38. 

Gas  checks,  7,  3,  13,  2,  21,  6. 

Gate,  17,  9. 

Catling  gun,  29,  2. 

Gauging,  4,  U,  17,  17,  28,  25. 

Gautier  range  finder,  30, 18, 

General  coeflicient,  gunpowder,  11, 
20,  12,  28. 

Gerdon  fermeture,  21,  15. 

Giant  powder,  14, 13. 

Gin,  26, 1. 

Glazing  gunpowder,  4,  12. 

Gordon  range  finder,  30,  20. 

Graining  gunpowder,  4,  11,  13,  3. 

Grains,  diameter  of,  10.  2, 12,  4. 

Granulation  of  gunpowder,  4,  10. 

Grape  shot,  16,  23,  25. 

Gravimetric  density,  9,  3. 

Grazed  zone,  30,  49. 

Grenades,  16,  20. 

Gribeauval  carriage,  32,  25. 

Grinding,  1.5,  21,  17,  14. 

Ground,  slope  of,  30,  51. 

Guide,  rocket,  16,  45. 

Gun,  1, 1; combustion  in,  8,  2,  11, 

1,  4;  form  of,  5,  1;  lift, 

25,1. 

Gun  construction,  theory,  19,  11,  23; 
Itractice,  15,  56. 

Gun  cotton,  14,  2,  8  ; detona- 
tion of,  2,  6. 

Gunpowder,  adapted  to  gun,  11,  7,  24, 
12,  16,  32,  13,  3,  6;  advan- 
tages of,  2,  II; characteristics, 

12,  2,  22; composition  of,  2,  10, 

9,2; concrete,  4,  11,16,21; 

fiat,  4,  12,   13,  5;  Fossano,  13, 

5; history  of,  13, 1;  hexag- 
onal, 13,  5;  ingredients,  3,1; 

machinery,   4,  2;  manu- 

ficture,  4.  1;  modern,  13,  6; 

modulus  of  qaickness,  12,  10, 

29;  —  pebble,  4, 12, 13,5; pris- 
matic, 4,  15,  10,  4,  11,  6,  13,  4,  6; 
products  of,  2,  10,  9.  6,  II,  29; 

-^reaction,  a,  loj  — KodmaB's, 


INDEX. 


13,  3; small  caliber,  «7,  9,  2S, 

21,  22;  smokeless,  3,  7,   14,  8, 

15,  88,  22;  sphero  hexagoual, 

13,  5;  work  of,  11.  10. 

Gustavus  Adolphus,  27, 1. 


Hale  rocket,  16,  46. 

Hall  rifle,  87,  2. 

Hammers,  15, 45. 

Hand  arms,  36,  1 

Hardening,  15,  22,  52; carbon,  15, 

15,  48; strains,  15,  55. 

Harness,  84,  6. 

Heat  of  gunpowder,  ^,  6,  9,  7; 

waste  of,  9, 10,  1 1,  8. 
Hebler,  system,  88, 19. 
Helhofite,  14,16. 
High  explosives,  8,  10,  14, 1; 

for  bursting  charge,   J6,  21; 

use  of,  14,  7,  19. 

History  of  ammunition,   87,  1; 

of  gunpowder,  13, 1; of  rifling, 

16,  8; of  shrapnel,  16,  30; 

of  small  arms,  87, 1,  88, 1, 16 

Hitting,  probability  of,  30,  27,  35,  43 

Hollow  of  wheel,  548,  24. 

Hooke's  law,  19,  22. 

Horse  and  harness,  84, 1. 

Hotchkiss  ammunition,  89,  20; 

brake,  88,  12;  field  carriage, 

89,  20; fuzes,  18, 14; guns. 

81,  16,  17; mounts    89,  1; 

rapid  fire  gun,  29,  21; revolv- 
ing cannon,  89,  14; projectile, 

16, 15,  17. 

Housing,  pressure  gauge,  7,  4. 

Howitzer,  1,  1; siege,  81,  18. 

Hydraulic  bufier,  88,  14,  83,  :  ;  

forgingpress,  15,  47; Jack,  85, 

1; motor,  4,  9,  15,  15,  33,  34,  47, 

17,  14. 

Hydro  pneumatic  carriage,  88,  .18. 

Hypothesis,  Barlow,  19, 2; Noble's, 

9,8. 

I. 

Ignition  of  gunpowder,  8, 1; and 

infl^mmAtioa  iu  guns,  1 1, 18. 


fuze. 


Igniting  charges,  18,  5. 
Impact,  center  of,  30,  23; 

16,  18,  18,  6,  11. 
Immovable  layer,  7,  1,  11,  9 
Incendiary  projectiles,  16,  22. 
Increasing  twist,  J6,  9,  IJ,  15. 
Incorporation  of  gunpowder,  4,  7,  16, 

44. 
Independence  of  function,  9,  1,  16, 

34,    18,  16,  19,  16,  81,  2,  19,  22,  88, 

23,  84,  6,  86.  3,  4,  87,  4,  88,  4,  15, 

89,  4.  8,  15,  24. 
Inertia  igniter,  18,  10,  16,  17. 
Inflammation  of  gunpowder,  8, 1; 

prism,  16,  -21. 

Ingots,  15, 34;  metals,  15,  U. 

Initial  tension,  19,  11,  23. 

Initial  velocity,  1,  2. 

Inspecting   instruments,    projectiles, 

17,  17. 
Interchangeability,  88,25. 
Internal  strain,  15,  21,  55,  19,  12. 
Interrupted  screw,  81,  11. 
Interrupter,  6,  12. 
Interstitial  volume,  9,  3. 

Iron  castings,  15,  24,  26,  27. 


Judson  powder,  14, 14. 
Jump,  80,  2,  3. 


Kalchoids,  15,  14. 

Kinetic  measures,  7,  9,  16. 

King  carriage,  8Si,  13. 

Krupp  fuze,  18,   15;  gun,  15,  15, 

81.  6,  9;  process,  15,  19;  

steel,  15,  15,  32. 


Lathe,  17,  11; 

13. 
Lance,  86, 1. 
Lands.  1,2. 
Leather,  84,  9. 
Lead,  projectiles,  16,  5,  24 
Lead  of  wheel,  88,  24. 
Lebel  powaer,  14, 18. 


variations  of,  17, 


INDEX. 


Le  Bouleng6  Telemeter,  30,  11; 

chronograph,  6,  6. 
Lee  rifle,  38,  7,  II. 
Lemoine  brake,  33, 19. 
Length  of  bore,  5,  2,  7,  II,  11,  IJ,  13, 

2,  19,  47. 
Levers  in  guns,  27,  6,  28,  6. 
Light  balls,  16,  22. 
Limber,  23,  27,  23,  2;  chest,  22, 

28 
Limiting  values  of  pressures,  19, 39. 
Line  of  departure,  J*0, 1; of  metal, 

1,  2; of  signt,  ao,  1. 

Liners,  19,  20. 

Liquation,  15, 16. 

Loam,  17,  3. 

Lock,  Springfield,  28,  16, 

Longitudinal  stress,  19,  16,  30. 

Longridge  gun,  19,  19. 


M. 

MacDonald,  Hale  rocket,  16,  45. 

Machines,  artillery,  25,  1;  guns, 

21,  1,  29,  I,  12. 

Magazine  arms,  27,  3,  28,  9,  13,  14. 

Maitland  formula  for  armor,  16,  38. 

Malleability  of  metals,  15,  23. 

Malleable  castings,  15,27. 

Mandreling,  15.  22,  19,  11. 

Mandrels,  forging,  15,  47. 

Manganese  in  steel,  15,  19. 

Mannlicher  rifle,  28,  12. 

Manometric  balance,  7,  8. 

Manufacture  of  ammunition,  27,  6; 
of  fuzes,  18,  IS;  of  gun- 
powder, 4,  5;  of  projectiles, 

17, 1; of  small  arms,  28,  24. 

Marking  gunpowder,  4, 13. 

Matches,  18,  1. 

Maxim  aut.  machine  gun,  29,  8; 

rapid  fire  gun,  29,  25. 

Mayewski's  experiment,  7,  9. 

Mean  error,  30,  24,  33; point  of 

impact,  30,  23; trajectory,  16, 

23,  30,  6. 

Mechanism,  small  arm,  28,  5. 

Megagraph,  6,  7. 

MeUing^,  15,24,  n,6. 


Metals  for  cartridges,  27,  5;  ord- 
nance. 16,  13; physical  prop- 
erties of,  15,  13;  useful  prop- 
erties of,  15,  15. 

Metallic  cartridges,  27,  2. 

Micrograph,  6,  8. 

Mildness,  coeflicient  of,  11, 19. 

Military  explosives,  2,  9. 

Mill  cake,  4,  8; gunpowder,  4, 1; 

train,  15,  43;  universal, 

15,  43. 

Milling,  17,  13,28,28. 

Mi  lis  metal,  15,  20. 

Mixing  gunpowder,  4,  7, 16,  44. 

Modulus  of  elasticity,  15,  4,  19,  22. 

Moistening    gunpowder,   4,   7 ; 
molds,  17,  2 

Molding,  17,  1,  10;  composition, 

17,  2; tools,  17,  6. 

Molded  gunpowder,  4,  10  ; 

press  for,  4,  15. 

Moncriefl  carriage,  22, 13, 

Morse  cartridge,  27,  5,  28,  22. 

Mortar,   1,  1,  21,  17,  19,22; car- 

riage,  23,  7;  fire,  formula;  for, 

20,  6,  8;  fuze,  18,  9;  wagon, 

22,  28. 

Mounts,  for  rapid  fire  guns,  29, 18. 

Mountings,  email  arm,  28,  5, 

Mu  ifi),  11,  19 

Mule,  24,  1. 

Muzzle  loading  projectiles,  5, 3, 16, 12. 


N. 

Napoleon  gun,  21,  4. 

Nasmyth  hammer,  15,  45. 

Natural  line  of  sight,  30,  2. 

Nave,  22,  22. 

Nickel  armor,  16,  43;  in  steel, 

15,  20. 
Nitrates,  3,  6,  12,29. 
Nitre,  3,  6. 
Nitro-benzine,  14,  15;  glycerine, 

14, 11. 
Niven's  method,  20,  25. 
Noble's  gauge,  7,  4; experiments, 

7,  16,  9,  1;  —  an(i  Abel's  law, 
9,8, 


INDEX. 


Nolan  range  finder,  30, 20, 
Non-metallic  cartridges,  fil,  2. 
Non-recoil  guns,  as,  18,  29,  1 ; 

mount,  29,  19. 
Nordenfelt    gunpowder,   4,    15;   

machine  gun,  89,  S; rapid  fire 

gun,  29,  24. 
Nucleus,  30,  6. 
Number  of  grains  varied,  10,  2. 


Oblong  projectiles,  advantages  of,  16, 

4. 
Obturating  primers,  18,  4. 
Oil  hardening,  15,  53,  57. 
Open  hearth  process,  15,  37; 

steel,  16,14,32. 
Orders  of  explosion,  3,  2,  4. 
Ordnance,  I,  1. 
Origin  of  motion,   .1,10. 
Oxidation,  rate  of,  15,  37;  scale 

of,  16, 17. 
Oxydizing  agents,  3,  6. 


P. 

Pack  horse,  84, 1. 

Palliser  gun,  ai,  5.  ' 

Parallax,  30,  11. 

Parrott  gun,  21,  5  ;   i)rojectile, 

16.  12. 

Parting  plane,  17,  4;  sand,  17,  3. 

Passive  resistances,  11,  8. 

Patterns,  17,  3,  7. 

Pebble  powder,  4. 12,  13,  5. 

Peep  sight,  30,  4. 

Percussion  caps,  18,  2; fuze,  18, 

11. 
Pemot  furnace,  15,  30,  41. 
Petroleum  fuel,  15,  38. 
Phi  dash(g)),  20,  22,  37,  50. 
Phosphorus  in  steel,  15, 19. 
Physical  constants,  24,  2,  28, 17;  

properties,  15,  1, 12,  20,  57. 
Pi  (FT),  coj^fficient,  11,  27,  12,  29. 
Picric  acid,  1  4,  17. 
Piemonte   S.  S.,  29,  17, 
Fiutles,  ^^,  9,  36.. 


Piping,  15,  21. 

Plane  table,  30, 14. 

Platforms,  '4a,  19. 

Pointing,  20,  1,  30, 1. 

Porter  bar,  16,  56. 

Ports,  22,  14. 

Potasaum  chlorate,  3,  7,  14, 16, 19. 

Potential,  »,  6,  9,  7;  work,  2,  6, 

II,  9,  15,      . 

Pouring,  17,  7. 

Powder  mills,  4, 1. 

Pratt  range  finder,  30, 17. 

Precautions  in  manufacture  of  gun- 
powder, 3,  5, 4, 1. 

Premature  explosions,  18,  19,  21,  14, 
28,6. 

Preponderance,  1,  2,  22,  8. 

Press  cake,  4,  7; forging,  16,  47; 

powder,  4,  9, 15. 

Pressure  curve,  9,  13,  11,  3,  12,  8, 
19,  46. 

Pressure,  exterior  limits  of,  19,  39; 

formula;,  Sarrau,  12, 8, 13; 

gauges,  7, 1,  5;  in  gun.  Noble 

and  Abel,  9,  11;  ■  high  explo- 
sives, a,  8, 14,  4; piston,  mass 

of,  r,  6. 

Primers,  14,  3,  18, 1,  3. 

Probability  of  fire,  30,  27. 

Probable  error,  30,  32; rectangle, 

30,  34; zones,  30,  33. 

Products  of  gunpowder,  2,  10,  11,  29; 

of  high  explosives,  2,  2,  14, 

4.  9,  12. 

Profiling,  28,  28. 

Profile  of  i)rojectile,  16, 16,  20,  9. 

Progressiveness,  10,  3,  11, 19. 

Progressive  range  finding,  30,  21. 

Projection,  angle  of,  20,  2. 

Projectiles  defined,  16,  1;  form 

of,  5, 3; manufacture  of,  1 7, 1; 

proof  of,  17, 16,  18. 

Proposed  magazine  arm,  2S,  13. 

Proportions  of  cannon,  5,  2,  9,  13,  13, 
2,  19,  6,  46. 

Puddled  steel,  15,  30. 

Pulls,  15,  44. 

Pulverizing  gunpowder,  4,  6, 

Funching  armor,  16,  36, 


iJ^i)E5t. 


Quadrant  an^le,  20,  2. 

Quenching  15,  22,  49. 

Quickness  of  gunpowder,  11,  7,24,  12, 

10, 12,  29. 
Quick  loader,  38, 13. 
Quick  match,  1 8, 1. 


Rackarock,  14, 15. 

Racking  armor,  16,  36. 

Radius  of  gun,  20,  1. 

Ramsbottam's  hammer,  15,47. 

Range,  20,  4  ; to  compute,  20,  36; 

finding,  30, 10; table,  30, 

8,  52. 

Rapidity  of  lire,  27,  2;  28,  1;  29, 1,  7, 
11,  16,  17,  26,  30,  61;  of  re- 
action, 2,  8. 

Rapid  firing  guns,  21,  1,  29,  l,  16. 

Reaction,  gunpowder,  2,  10; gun 

cotton,  14,  9; nitro-glycerine, 

14,  12; rapidity  of,  2,  8. 

Re- annealing,  15,  67. 

Recoil,  angle  of  greatest,  22,  9; of 

cannon,  11, 18,  19,  19; control 

of,  22, 11;  —  energy  of,  19, 19,  2'^, 

3; extent  of,  22,  7,  11, 16;  

force  of,  22,  5; mount,  29,  19; 

periods  of,  22,  3; pheno- 
mena of,  22,  8; rotation   due 

to,  22,  8; small  arms,  28,  16; 

in  testing  metals,  15,  3; 

work  of,  15,  5,  22,  4. 

Refining  steel,  15,  52. 

Regenerator,  15,  39.  . 

Reheating  furnace,  15,  45. 

Remeltlng  iron,  15,  24, 

Reinforce,  1,2. 

Resistance  of  air,  20,  8,  16;    of 

cannon,  19,  fi,  31,  3:5;  passive, 

11,  8;  of  primers,  18,  4. 

Retardation,  coefficient  of,  16,  2. 

Reverberatory  furnace,  15,  25. 

Revolvers,  28,  23. 

Ricqs  register,  7,  15. 

Rifle,  28,  1. 

Rifling,  1,  2,  16,  8,  28,  3,  27. 


Right  line  method,  30,  41,  45. 

Rigidity  of  trajectory,  20,  24. 

Rimfire  cartridge,  27,  3. 

Rimless  cartridge,  28,  23. 

Riser,  17,  9. 

Rockets,  16,  44. 

Rodman's  gauge,  7,3; gun,  19,12; 

improvements  in  gunpowder, 

13,  3; velocimeter,  6, 13, 7, 12. 

Rolls,  4,  3, 

Rolling  mill,  15,  43;  — ^  table,  17, 17. 

Rotating  bands,   17,  15;  device, 

11,  16,  16,  12,  15. 
R^ation  of  projectile,  11,  16,  16, 12. 
Rotary  energy,  16,  3;  furnace, 

15,  37,  41. 
Rotten  steel,  15,  18. 
Rumford's  gauge,  7,  2. 
Rupture  of  shells,  16,  19. 
Russell's  interrupter,  6, 13. 


Saber,  26,  2. 

Safe  space,  20,  39,  43,  30,  51. 

Saltpeter,  3,  6. 

Sand,  molding,  17,  3. 

Sarrau,   application,  12,  21,  28 ;  

formulae,  12,  1;  on  pressure 

gauge,  7,  8. 

Sawyer  canister;  16,  25. 

Schulhofl"  magazine  rifle,  28, 13. 

Screw  guns,  21,  17;  interrupted, 

21,  10. 

Sea  coast  cannon,  21,  20; car- 
riage, 23,  5; fuze,  18.  9. 

S6bert's  projectile,  7,  10; veloci- 
meter, 6.  13,  7,  13. 

Sectional  density,  16, 1,  28,  21. 

Segment  shell,  16,  33. 

Segregation,  15.  16,  59. 

Sensitiveness  of  high  explo.sives,  14, 2. 

Set  of  metal,  15,  3; of  wheel,  22, 

24. 

Shafts,  22,  28. 

Sheaf  of  dispersion,  16,  23,  30,  6. 

Shearing  plane,  27,  4. 

Shear  steel,  15,  30 

Shells,  16,  18;  bursting  charges, 

14,  7, 19, 16,  20,  33,  19, 17. 


10 


1NDE5^. 


Shields  for  guns,  16,  41,  23,  6. 

Shock,  explosion  by,  8,  2,  14,  3,  7,  12, 
15,  16,  16,  21,  18,  11. 

Shortening  bore,  7,  y. 

Shrapnel,  16,  23,  26; early,  16, 30; 

fire,  16,  34. 

Shrinkage  in  cannon,  15,  21,  58,  19, 
12, 15,  23,  41. 

Shuts.  15,  44. 

Side-box,  maxim,  29,  27. 

Siege  cannon,  21,  17;   carriage, 

«3,  3. 

Siemen's  furnace,  15,  C9; regene- 
rator, 16,  3!). 

Sights,   20,   1,   28,  4,  20,   30,  1;    

angle  of,  20,  2;  field,  30,  3; 

heavy  guns,  30, 3; line  of, 

20,  1;  plane  of,  20,  4;  

radius,  20, 1; small  arm,  28, 4. 

Signal  time,  6,  1,  12. 

Silico-Spiegel,  15, 18,  28. 

Silicon  as  fuel,  15,  35;  in  steel, 

15,18. 

Similitude,  principle  of,  1^,  14. 

Sinclair  check,  22,  12. 

Singletree,  22,  27,  24,  5. 

Sinking  head,  15,  34,  58,  17, 10, 15. 

Single  cylinder,  strength  of,  19,  6,  31. 

Size  of  grain,  10,  2,  11,  4. 

Slide  rest,  17,  11. 

Sling  cart,  25,  2. 

Slow  match,  18, 1. 

Small  arms,  1,  1,  28, 1;  ammuni- 
tion, 27,  1, 9;  manufacture  of, 

28,  24. 

Small  caliber,  28,  2,  20. 

Smokeless  gunpowder,  3,  7,  14,  15, 
28,  22. 

Soaking  pits,  15,  43. 

Sodium  nitrate,  3,  6. 

Solid  head  cartridge,  27,  5. 

Solid  shot,  16. 18. 

Special  irons,  15,  27. 

Specific  gravity  of  gunpowder,  9,  3; 
of  iron,  16,  24. 

Specific  volume,  2,  7,  9,  3,  7. 

Spheres  of  action,  14,  5. 

Spherical  case.  16,  31; density,  12, 

31,  16,6,  28,21. 


Spiegeleisen,  15,  28. 

Spindles,  lathe,  17,  11. 

Sprengel  mixtures,  14, 16. 

Springfield  rifle,  28,  15. 

Stationary  carriages,  2'4, 1. 

Stadia,  30, 13. 

Static  measures,  7,  2 

Steam,  comparison  to,  11,1; test, 

17,17. 

Steel  castings,  15,  42;  cast  can- 
non, 15,  58;  classification  of, 

15,  13, 18; composition  of,  15, 

17; constitution  of,  15, 16; 

manufacture  of,  15,  30;  me- 
chanical treatment  of,  15,  4  ;  

molecular  treatment  of,  15,48; 

projectiles,  16,  6; projectiles, 

manufacture,  17,  14; proper- 
ties under  stress,  15, 22; struc- 
ture of,  16,  20,  49;  working 

properties,  15,  22. 

Stock,  cannon,  22, 3, 25; rifle, 28, 3. 

Stone  projectile,  16,  5. 

Store  wagon,  22,  29. 

Strain  diagram,  15,3,8; equalizing, 

19,  9,  19,  23; internal,  15,  21, 

55,    19,    12;    as   function    of 

radius,  19,  3,  29;  on  gun,  5,  2, 

16,3,  19,1. 

Strength  of  cannon,  5, 1, 2,  1 9, 6, 31, 33; 

of  explosives,  2,  6; of  gun 

construction,  coeflicient  for,  II, 
21. 

Stress  and  strain,  16, 1, 19,  22;  in 

guns,  5,  2,  16,  3, 19, 1. 

String  measure,  30,  24. 

Structure  of  projectiles,  16, 17. 

Studded  projectile,  16,  12. 

Successive  means,  method  of,  30,  21; 
shortening  of  bore,  7,  11. 

Sulphur,  3, 1; in  steel,  15,  20. 

Supply  train,  '-i'-i,  29. 

Surface  of  gunpowder,  8, 1,  10, 1. 

Sweep  molding,  17,  3,  5 

Swiss  method,  30,  27. 

Sword,  26,  1. 

Sympathetic  detonation,  2,  5. 

System  of  artillery,  21,  3;  at  rest, 

etc,  19, 13,  36. 


INDEX. 


11 


Tarage,  7,  7. 

Targets,  animate,  30, 48;  ——  comput- 
ing, 30,  26;  velocity,  6,  14. 

Team,  arrangement  of  horses,  24,  5. 

Telescopic  sight,  30,  3. 

Telemeters,  30,  11, 

Temperature  of  ignition,  8,  1,  14,  3; 

of  explosion,  2,  8,  9,  8;  

scale  of,  1,  3. 

Tempering,  15,  52. 

Tenacity,  15, 10. 

Testing  cannon    metal,   J  5,  57;    

machines,  16, 1,5; projectiles, 

17,  18. 

Test  piece,  form  of,  16, 2; record, 

15,  2,  8. 
Thickness  of  cannon,  5,  2,  9, 13,  19,6, 

19,  45,  46. 
Thrusting  arms,  86,  1. 
Thurston  machine,  15,  6. 
Tilted  steel,  15,  30. 
Time  of  flight,  30,  40,  41, fuze,  16, 

18,  18,  6,  10;  limits,  6,  8;  

of  maximum,  13, 11. 

Tire  rolling,  15,  44. 

Tolerance,  4, 11,  17, 17. 

Tonite,  14,  9. 

Torpedo  shells,  14,  8,  16,  20,  31, 18. 

Torsional  testing,  16,  6. 

Trajectory  in  air,  30,  18;  curva- 
ture of,  1,  3,  30,  23;  elements 

of,  30,  30; flatness  of,  1,  3.  30, 

23,  40,  38,  20,  30,  35,  30;  mean 

radius  of  curvature,  30,  23;  

rigidity  of,  30,  24;  in  vacuo. 

30,6. 

Traveling  trunnion  bed,  33.  (. 

"Treatment"  of  cannon,  15,  57. 

True  mean  error,  30,  33,  41. 

Trunnions,  inclination  of,  30,  2. 

Tubular  magazines,  38, 10. 

Tuning  fork,  6,  12,  7,  13. 

Tumbling  barrels,  4,  4;  of  pro- 
jectiles, 16,  3. 

Turning  angle,  33,  25. 

Twist,  10,  9, 


U. 

U,  path  of  projectile,  11, 10, 14,  13, 1. 
Units  of  measure,  1,  3. 

V. 

Vacuo,  trajectory  in,  30,  6. 

Value  of  explosives,  3,  8,  14,  2. 

Variables,  experimental,  9, 1. 

Varying  elasticity,  19,  9. 

Velocimeters,  6,  i,  7,  9; Benton, 

6,  3;  classified,  6,  2. 

Velocities  defined,  1,  2;  final,  30, 

17;    formula;,   13,  5,  12;  

targets,  6, 14. 

Vents  11, 18,  31, 13; direction  of, 

18,  3;  rocket,  16,  44. 

Vertex,  height  of,  30,  36;  prin- 
ciple of,  30,  42. 

Very's  formula  for  armor,  16,  41. 

Vesiculation,  15,  21. 

Volumes  of  expansion,  11, 12. 

Vulnerability,  30,  50. 

W. 

Wagon,  mortar,  33.  28; store,  J5J5, 

29. 
Washed  metal,  15, 19. 
Waste  of  energy,  9, 10,  11,  8. 
Water  on  high  explosives,  14,  5,  6; 

annealing,    15,   54;  cap, 

18,9. 
Weather,  30,  9,  30,  10. 
Weaver  formula  for  armor,  16,  42. 
Weight  of  cannon,  6,  1,  19,  19; of 

charge,   Jl,  13,  15,  13,  16,  32,  38, 

21;  distribution  of,  «3,  4,  34, 

2,  38,  17; of  projectile,  16,  8. 

Weld  steel,  15,  14. 
Weldability  of  metals,  15,  23. 
Weldon  range  finder,  30,  16. 
Wertheim's  coefficient,  19,  2,  3,  25. 
West  Point  target,  6, 15. 
Whitvvorth's    forging   press,   16,    47; 

projectile,    16,    12,    17;  

steel,  16, 15,  34. 
Wheel  mills,  4,  7;  principles  <jf, 

33,  21. 


12 


INDEX. 


Wheeled  carriages,  23,  2. 
Wiener's  powder,  4,  iO. 
Wiliiston  harness,  24,  8. 
Winchedter  magazine  rifle,  28, 10. 
Windage,  1,  2. 
Wind  and  accuracy,  30,  9. 
Wire  drawing,  15, 44; wound  can- 
non, 19,  17. 
Woodbridge  gun,  19,  18. 
Woods,  physical  properties  of,  16, 11 . 


Work  of  gunpowder,  3,  6,  9,  7, 11, 10. 
Wrapped  metal  cartridge,  87,  7. 
Wrought  iron,   manufacture,  16,  29; 
projectiles,  16,  5. 


Zalinski  gun,  10,  3,  14,  8. 
Zones  in  collective  fire,  30,  49. 
Zones,  probable,  30,  33. 


I. — DEFINITIONS. 


-  07  THr: 


^TJKITEBSIT 


CHAPTER  I, 


DEFINITIONS. 

Ordnance. — A  general  terra  usually  applied  only  to  the 
material  of  Artillery,  but  embracing  also  all  warlike  stores 
made  according  to  prescribed  regulations  or  ordinances. 

Fire  Arms. — Offensive  weapons  used  to  throw  projectiles 
by  means  of  explosives.     They  are  divided  into — 

1.  Cannon. — Heavy  fire  arms  requiring  carriages  to  sup- 
port and  to  transport  them. 

2.  Small  Arms, — Which  can  be  carried  by  men. 
Cannon  are  divided  into — 

Guns. — Or  relatively  long  cannon.  Gun  is  used  as  a  gen- 
eral term  for  all  fire  arms.  It  has  probably  the  same  root 
as  engine,  meaning  a  machine. 

Howitzers.. — Comparatively  short  cannon. 

Mortars. — Very  short  cannon. 

NOMENCLATURE. 

Bore. — That  part  of  a  cannon  which  is  bored  out.  It  in- 
cludes— 

1.  The  cylinder  or  principal  portion  of  the  bore.' 

2.  The  seat  of  the  charge,  or  the  part  occupied  by  the 
powder.  This  may  be  either  a  continuation  of  the  cylinder 
terminated  by  a  plane  or  curved  surface;  or  a  cha?nder,  the 
diameter  of  which  differs  from  tha*  of  the  cylinder  of  the 
bore.  For  breech  loaders,  the  chamber  is  divided  into  the 
powder  chamber  and  the  shot  chamber. 

Caliber. — The  diameter  of  the  cylinder  of  the  bore.  It  was 
formerly  expressed  by  the  weight  of  the  inscribed  sphere. 


I.  — DEFINITIONS. 


For  cannon,  this  was  the  weight  in  pounds  of  the  cast  iron 
shot;  for  small  arms,  the  number  of  leaden  balls  required  to 
weigh  a  pound. 

Rifling. — Cutting  spiral  grooves  in  the  surface  of  the  bore, 
so  as  to  give  to  the  projectile  a  motion  of  rotation  at  right 
angles  to  that  of  translation. 

Lands. — The  ridges  left  between  the  rifle  groves.  The 
caliber  of  rifles  is  usually  measured  between  lands. 

Chase. — The  long  conical  portion  of  a  cannon  in  rear  of 
the  muzzle. 

Reinforce. — The  thick  portion  of  the  body  over  and  imme- 
diately m  front  of  the  seat  of  the  charge. 

Breech. — The  mass  of  metal  in  rear  of  the  plane  of  right 
section  at  the  base  of  the  charge. 

Line  of  Metal. — The  intersection  of  the  upper  surface  of 
the  piece  by  an  axial  plane  perpendicular  to  the  axis  of  the 
trunnions. 

Dispart. — The  difference  between  the  semi-diameters  at 
the  muzzle  and  at  the  breech. 

Preponderance. — The  difference  between  the  moments  of 
the  weight  in  front  of,  and  in  rear  of,  the  trunnions. 

Windage. — This  is  properly  the  difference  between  the 
area  of  right  section  of  the  cylinder  of  the  bore,  including 
the  grooves,  and  the  maximum  parallel  area  of  right  section 
of  the  projectile. 

It  is  usually  expressed  in  linear  units  as  the  difference 
between  the  diameter  of  the  cylinder  of  the  bore  and  the 
diameter  of  the  projectile. 

VELOCITIES. 

Muzzle  or  Initial  Velocity. — Is  the  maximum  velocity  of 
the  projectile  after  leaving  the  piece, 


t. — BEFmiTlONS. 


Remaining  Velocity. — Is  that  at  any  point  of  the  trajec- 
tory. 

Terminal  Velocity. — Is  that  at  the  point  of  impact. 

The  greater  the  velocity  at  any  instant,  the  more  flat  does 
the  trajectory  become;  and,  therefore,  the  greater  is  the 
probability  of  striking  a  vertical  object  at  an  unknown 
distance.     (See  note  1,  page  5.) 

The  horizontal  distance  over  which,  under  given  condi- 
tions, a  vertical  object  would  be  struck,  is  called  the  dan- 
gerous space  for  that  object. 

UNITS    OF    MEASURE. 

Those  used  in  English  speaking  countries  are  unfortun- 
ately numerous  and  are  apt  to  cause  confusion. 

Units  of  Temperature. 

Throughout  this  work  the  temperatures  are  expressed  in 
degrees  centigrade. 

Units  of  Length, 

Yards. — For  ranges  of  projectiles. 

Feet. — For  measuring  velocities  and  the  chords  and  alti- 
tudes of  trajectories. 

Inches. — For  the  internal  dimensions  of  guns  and  for  all 
dimensions  of  their  projectiles.  The  decimal  sub-division 
of  the  inch  is  generally  employed. 

Units  of  Weight, 

Tons. — For  cannon,  1  ton =2240  lbs. 

Pounds. — For  large  projectiles,  for  their  charges  and  for 
measuring  the  pressures  (per  square  inch)  of  the  gases  of 
fired  gunpowder. 

In  England,  pressures  are  measured  in  tons  per  square 
inch;  in  France,  in  kilogrammes  per  square  centimetre;  else- 
where on  the  continent  of  Europe  in  atmospheres. 


t. — MFiNitioNS. 


Grains  Troy. — For  bullets  and  powder  charges  of  small 
arms  7000  grains  troy=l  lb.  avoirdupois. 

g  is  generally  taken =32.2  lbs.,  which  is  nearly  its  value  at 
London. 

Unit  of  Energy  and  Work, 
Foot  tons=foot  pounds-r2240. 

USEFUL   MECHANICAL    FORMULAE. 

s 


Uniform  motion,  v=- 

ds 
Varied    motion,  v—  —r: 


Uniformly  varied  motion,  v=-aJ<^  a-k  =  a-fj  h—  — 

% 

.        .  dv       d^s 

Acceleration,  af= -T- = -To- . 
at       dt^ 

Intensity  of  a  motive  force,  I=Ma. 

Intensity  of  an  impulsive  force,  I^-^MV, 

Measure  of  work,  Q=Wh—flds, 

Measure  of  energy,  E=  ^f^^ 

Time  of  oscillation  of  a  simple  pendulum,  t=;rA  / — 

ABBREVIATIONS. 

S.  B. — Smooth  bore. 

R.— Rifle. 

M.  L. — Muzzle  loading. 

B.  L. — Breech  loading. 

C.  I. — Cast  iron. 

W.  I. — Wrought  Iron. 
S._Steel. 

The  caliber  is  placed  first.     Example: 
8  in.  B.  L.  R.  S. 


1.— i>EpmiTtoNS. 


15  in.  S.  B.  C.  I.,  etc. 

W.  w. — Weight  of  larger  and  smaller  of  two  masses  consid- 
ered; as  of  piece  in  regard  to  projectile,  or  of  projectile  in 
regard  to  charge  of  powder. 

V.  V. — Initial  and  remaining  velocities. 

p. — Intensity  of  gaseous  pressure  per  unit  of  area. 

r.  d. — Radius  and  diameter  of  the  cylinder  of  the  bore,  or 
of  the  projectile  according  to  context. 


Note  1.  From  Michies  Mechanics,  Article  94,   we  have  — =  '^  ^^ 
See  also  Chapter  XX,  p.  22.  p         "v      , 


!I. — EXPLOSIVE    AGENTS. 


CHAPTER   II. 

EXPLOSIVE  AGENTS. 

Explosion. 

Is  a  name  given  to  a  series  of  phenomena  resulting  from 
two  general  causes. 
Causes  of  Explosion. 

I.  The  rapid  conversion  of  a  solid  or  liquid  to  a  gaseous 
state.  This  conversion  is  accompanied  by  the  evolution  of 
heat,  due  to  the  nature  of  the  chemical  reaction  involved. 

II.  The  rapid  dilatation  of  a  mixture  of  gases  by  the  heat 
evolved  in  their  combination.  Such  explosives  are  not  yet 
generally  employed  in  warfare  and  are  not  herein  considered. 
Products. 

The  gases  evolved  in  conversion  are  principally  CO2  and 
CO.     These  result  from  the  more  or  less  perfect  combustion 
of  carbon,  which  enters  into  every  military  explosive  under 
circumstances  intended  to  facilitate  its  oxidation. 
Dissociation. 

The  tendency  at  high  temperatures  of  CO2  and  other  com- 
plex products  to  occur  in  simpler  forms,  as  CO  +  O,  is  sup- 
posed by  Berthelot  to  exert  a  powerful  influence  upon  the 
corresponding  pressures. 

Dissociation,  as  this  phenomenon  is  called,  whether  it  pre- 
vents the  formation  of  the  complex  product  or  destroys  it, 
increases  the  specific  volume  of  the  gaseous  products;  but, 
since  Mariotte's  law  has  been  proved  not  to  hold  for  pres- 
sures ^  of  those  found  in  fire  arms,  it  is  supposed  that  the 
loss  of  heat  from  imperfect  combination,  or  from  work  done 


II. — EXPLOSIVE    AGENTS. 


in  breaking  up  the  molecules  already  formed,  exceeds  in  its 
effect  upon  the  resultant  pressure  the  increase  of  specific 
volume  cited.  External  causes  may  subsequently  decrease 
the  temperature  and  permit  recombination  with  a  relative 
increase  of  pressure. 

It  is  found  that,  when  the  conversion  yields  a  large  pro- 
portion of  CO,  the  violence  or  sharpness  of  the  explosion  is 
increased.  This  is  supposed  to  be  due  to  the  rigidity  or 
stability  of  this  gas  against  diSvSOciation. 

H2  O  is,  by  some,  supposed  to  be  subject  to  dissociation 
at  the  temperatures  found  in  explosions.     (See  Bloxam,  Arts. 
36,  68,  311,  Note.) 
Firing. 

The  proximate  cause  of  the  reaction  resulting  in  an  explo- 
sion is  always  the  absorption  by  some  portion  of  the  explo- 
sive of  heat  sufficient  to  raise  its  temperature  to  the  point 
necessary  to  start  the  conversion. 

The  source  of  heat  may  be  external;  or,  as  in  spontaneous 
decomposition,  internal. 

The  means  by  which  the  temperature  of  the  explosive  is 
raised  to  the  critical  point  may,  in  general  terms,  be  called 
firing. 

Firing  generally  results  from  the  transformation  of  kinetic 
energy  into  heat  as  a  result  of  arresting  the  motion  of  either 
molar  or  molecular  masses. 

Almost  all  explosives  may  be  fired  by  molar  shock,  if  it  be 
concentrated  on  a  mass  of  the  explosive  which  is  sufficiently 
small.     (Bloxam,  Arts.  309,  434,  538). 
Orders  of  Explosion. 

The  energy  of  molecules  in  motion  depends  principally 
upon  their  velocity;  and  the  external  work  done  in  stopping 
them,  upon  their  stability  of  composition.  When  an  explo- 
sive is  fired  by  contact  with  incandescent  matter,  as  by  a 
flame  consisting  of  molecules  of  COg,  C,  etc.,  moving  with 


II. — EXPLOSIVE    AGENTS.  3 

relatively  low  velocities,  the  explosive  is  said  to  be  ignited^ 
and  the  explosion  is  called  low  or  of  the  second  order. 

When  fired  as  by  fulminate  or  gun  cotton,  the  conver- 
sion of  which  yields  a  large  proportion  of  molecules  of  CO, 
moving  with  a  very  great  velocity,  the  explosive  is  said  to 
be  detonated,  and  the  explosion  is  called  high  or  of  \.\\&  first 
order.  ■  Explosives  which  readily  detonate  are  called  high 
explosives. 

Example,  Gun-cotton  when — 

Order. 

Ignited         j  unconfined;  burns  quietly — 

^  *  *  '  (  confined;  explodes  like  gunpowder 2nd 

unconfined       )        i   j         vu 

[  explodes  with  great 


f      violence 1st 


Detonated . . .  -j  or 

(        confined; 

The  distinction  between  the  two  orders  of  explosion  is 
only  conventional;  the  phenomena  in  practice  appearing 
often  to  partake  of  the  nature  of  both  orders. 

This  may  explain  certain  anomalies  observed  in  mining 
and  in  artillery.  In  mines,  when  the  charges  are  large,  the 
high  pressure  resulting  from  the  initial  explosion,  if  at  a 
point  considerably  beneath  the  surface  of  the  charge,  is  sup- 
posed to  cause  the  detonation  of  the  remainder.  In  cannon 
the  mixing  of  quick  with  slow  powder  produces  a  similar 
effect. 


BERTHELOT  S   THEORY    OF   EXPLOSIVES. 

Origin  of  Reactions. 

"  Every  explosion  must  be  referred  to  some  initial  increase 
of  temperature  transmitted  from  particle  to  particle  on  the 
surface  of  an  explosive  wave.  This  wave  raises  successively 
all  portions  of  the  explosive  to  the  temperature  of  convei- 
sion. 


II. — EXPLOSIVE    AGENTS. 


Propagation  of  Eeactions. 

Two  limiting  conditions  are  supposed  to  result,  viz.: 

1.  The  condition  of  combustion. 

2.  The  condition  of  detonation. 

These  are  progressively  interchangeable  in  different  de- 
grees, according  as  the  amplitude  and  velocity  of  vibration 
of  the  particles  forming  the  surface  of  the  explosive  wave 
are  increasing  or  diminishing. 

Combustion. 

I.  The  condition  of  combustion  depends  upon  a  reduc- 
tion of  temperature  from  the  free  expansion  of  a  portion  of 
the  gases  resulting  from  the  initial  explosion. 

Successive  portions  of  the  explosive  will  thereupon  be 
heated  to  the  temperature  of  decomposition  with  a  velocity 
depending  upon  various  conditions;  this  velocity,  compared 
with  that  of  detonation,  is  slow. 

Detonation. 

II.  On  the  other  hand,  the  condition  of  detonation  de- 
pends upon  an  initial  shock,  too  sudden  (sharp)  to  permit  of 
molar  motion  of  the  particles  of  the  explosive.  It  is,  there- 
fore, transmuted  into  heat  which  may  raise  the  contiguous 
molecules  to  the  temperature  of  conversion.  The  result- 
ing gases  arc  projected  as  a  single  (not  periodic)  explosive 
chemical  wave  traveling  throughout  the  successive  layers  of 
the  unexploded  mass.  This  wave  transforms  its  energy  into 
heat  at  each  impact,  and,  by  virtue  of  its  acceleration,  raises 
each  of  the  successive  layers  more  rapidly  to  the  tempera- 
ture of  conversion. 

Origin  of  Orders  of  Explosion. 

The  order  of  the  resulting  explosion  will  depend  upon  the 
velocity  with  which  the  reaction  is  propagated;  /.  ^.,  the  velo- 
city of  the  wave  surface  described. 

The  velocity  of  the  wave  surface  will  depend — 


n. — EXPLOSIVE   AGENTS. 


1.  Upon  the  molecular  velocit}^  of  the  reaction;  /.  ^.,  the 
rate  of  conversion  under  constant  conditions. 

2.  Upon  conditions  which  prevent  the  free  expansion  of 
the  gases  formed. 

3.  Upon  the  mass  and  initial  temperature  of  the  explo- 
sive; these  affect  the  rate  of  cooling. 

The  last  two  conditions  may  be  neglected  when,  as  with 
the  high  explosives,  the  first  is  fully  satisfied. 
Influence  of  Detonator. 

It  is  seen  that  detonation  depends  upon  a  chain  of  causes 
which  results  from  the  nature  of  the  initial  explosion.  Herein 
lies  the  importance  of  the  nature  of  the  detonator,  its  mass, 
and  the  nature  of  its  own  explosion. 

Its  conversion  should  be  rapid  and  evolve  abundant  heat. 
The  mercuric  fulminate  is  the  detonator  which  is  preferably 
employed.     It  is  less  violent  than  NCI,  but  yields  more  heat 
by  its  explosion  and  also  much  CO. 
Influence  of  the  Explosive  detonated. 

Detonation  depends  upon  the  physical  condition  of  the 
explosive.  Its  sensitiveness  generally  diminishes  as  its  den- 
sity and  elasticity  increase,  since  the  shock  is  distributed 
over  a  greater  mass." 

SYMPATHETIC    DETONATION. 

Conditions. 

The  instability  of  the  high  explosives  renders  their  con- 
tact unnecessary  when  the  continuous  detonation  of  several 
charges  is  desired.  The  maximum  interval  permitting  ''sym- 
pathetic detonation,"  or  "detonation  by  influence,"  and  the 
order  of  this  detonation,  depend  upon  the  elasticity  of  the 
intervening  medium,  the  mass  of  the  primitive  charge,  and 
the  order  of  its  explosion. 
Examples. 

Calling  w  the  weight  of  the  primitive  charge  in  pounds, 
and  d  the  maximum  interval  in  feet — 


n. — EXPLOSIVE    AGENTS. 


In  water,  d=S  w. 

On  a  firm  soil,  (/=5  w. 

On  an  iron  rail,  ^=10  w. 

When  discs  of  compressed  gun-cotton  are  in  contact,  the 
velocity  of  detonation  is  said  to  be  over  3J  miles  per  second 
when  the  discs  are  wet,  and  less  than  3J  miles  per  second 
when  they  are  dry.  The  incompressibility  of  the  water  assists 
in  transferring  the  shock. 

STRENGTH    OF    EXPLOSIVES. 

The  strength  of  an  explosive,  or  its  mechanical  efificiency, 
may  be  analyzed  by  reference  to  1,  its  potential;  2,  its  force; 
3,  the  molecular  velocity  of  its  reaction. 

1.  Potential. 

The  potential  of  an  explosive  is  the  maximum  work 
which  a  unit  weight  of  it  can  perform.  It  is  measured  by 
the  product  of  the  quantity  of  heat  liberated  by  the  reaction, 
and  the  mechanical  equivalent  of  heat;  or,  Q= J  x  H. 

The  potential  is  independent  of  the  process  of  conversion, 
provided  it  be  complete  and  its  products  be  constant. 

In  practice,  these  products  often  vary  with  the  circum- 
stances under  which  they  are  formed,  so  that  the  potential 
realized  will  also  vary. 

Only  a  portion  of  the  potential  can  be  realized  in  prac- 
tice, depending  upon  the  volumes  of  the  gases  produced, 
their  specific  heats,  and  the  difference  between  the  tempera- 
tures at  which  they  are  formed  and  to  which  they  are  ex- 
panded. 
Examples.* 

Theoretical  potentials,  in  foot  tons,  resulting  from  the 
conversion  of  one  pound  of  each  of  the  following  sub- 
stances: 


*  It  is  required  that  only  the  general  principles  illustrated  by  this  and 
following  tables  shall  be  committed  to  memory. 


II. — EXPLOSIVE    AGENTS. 


Name.  Foot  Tons.  Proportion. 

Blasting  powder 391  1.0 

Cannon       "      609  1.3 

Sporting     «      642  1.4 

Gun-cotton 716  1.8         1.0 

Dynamite  No.  1 884  2.3         1.3 

Explosive  Gelatine 1,235  3.2         1.8 

Nitro-glycerine 1,282  3.3         1.8 

Chloride  of  Nitrogen 216  0.5 

Anthracite  coal 6,170         13.0 

The  greater  potential  of  coal  is  due  to  its  composition  and 
to  there  being  no  loss  of  energy  expended  in  converting  in- 
to gas  the  compounds  of  oxygen  contained  in  the  other  sub- 
stances. 
2.  Force. 

The  force  of  an  explosive,  or  the  pressure  per  unit  of  area 
due  to  the  explosion  of  a  unit  of  weight  in  a  unit  of  volume, 
may  be  calculated  on  theoretical  grounds  from  the  formula,* 

In  which  v^  is  what  is  known  herein  as  the  specific  volume  of 
the  gas,  viz.:  the  volume  in  litres  of  the  gases  resulting  from 
firing  one  kilogramme  of  powder,  taken  at  0°  C,  and  at  the 
pressure  p^  of  one  atmosphere ;  and  c  is  the  specific  heat  of 
the  gas. 

But  the  uncertainty  attending  the  application  of  the  laws 
of  Mariotte  and  Gay-Lussac  to  such  high  pressures  as  exist 
in  cannon,  and  the  doubt  as  to  the  nature  and  state  of  the 
products  of  explosion  at  the  epoch  of  maximum  pressure 
have  caused  instrumental  measurements  of  pressure  to  be 
preferred. 

Examples. 

The  following  table  shows  in  round  numbers  the  relative 
force  of  the  explosives  named. 


*  For  the  deduction  of  this  formula  see  page  11. 


II. — EXPLOSIVE    AGENTS. 


The  detonation  of  gunpowder  was  accomplished  by  mix- 
ing it  with  dynamite. 

Eelative  Force. 
Explosive.  1st  Order.       Snd  Order. 

Gunpowder 4.0  1.0 

Gun-cotton 6.0  3.0 

Nitro-glycerine 10.0  5.0 

The  force  of  a  mixture  of  high  explosives  is  proportional 
to  the  sum  of  the  products  of  the  force  of  each  constituent 
by  the  corresponding  fractional  part  of  the  whole  mass. 

A  remarkable  property  of  gunpowder  (to  be  referred  to 
hereafter)  is  that,  however  its  potential  may  vary  with  its 
composition,  the  force  of  all  compositions  is  sensibly  con- 
stant. The  specific  volume  of  the  gases  formed  seems  to 
vary  inversely  with  the  quantity  of  heat  evolved  in  their 
formation. 

3.  Rapidity  of  Reaction. 

The  temperature  increases  with  the  rapidity  of  the  reac- 
tion. This  depends  upon  the  affinity  between  the  combin- 
ing molecules,  and  largely  upon  the  state  of  aggregation 
of  the  exploding  mass,  in  so  far  as  it  affects  the  distances 
between  them. 

In  certain  high  explosives,  the  rapidity  of  the  reaction 
causes  so  high  a  temperature  that  the  gaseous  products  are, 
as  it  were,  shot  against  the  w^alls  of  the  envelope  with  such 
velocity  that  the  effect  seems  due  rather  to  a  physical  shock, 
than  to  the  elastic  pressure  of  a  confined  gas.  With  such 
explosives  tamping  is  relatively  unneccessary. 

VALUE    OF   EXPLOSIVES. 

As  a  general  rule,  the  value  of  an  explosive  depends: — 
1.  Mechanically;  upon  its  primitive  state  of  aggregation,  in 

so  far  as  this  affects  the  ease  of  handling  it  in  loading;  also 

upon  its  density. 


II. — EXPLOSIVE    AGENTS. 


V  H 
2.  Chemically;  upon  the  value  of  the  ratio  —2 — z=iv^T^ 

If,  when  this  is  great,  the  conversion  is  sufficiently  rapid,  a 
high  and  elastic  pressure  will  succeed  the  initial  shock;  this 
pressure  will  be  well  sustained,  since  the  cooHng  effect  of 
the  envelope  will  be  relatively  small. 

The  potential  of  an  explosive  is  thus   seen  to  be  the 
measure  of  its  power  of  sustaining  a  given  force  or  pres- 
sure. 
Examples. 

The  relative  importance  of  potential,  force,  and  rapidity, 
depends  upon  the  use  made  of  the  explosive. 

In  order  to  burst,  we  use  one  of  high  force  and  density, 
acting  locally  like  an  hydrostatic  pressure. 

Chloride  of  nitrogen  detonates  with  such  rapidity  that  it 
may  simply  pulverize  the  surface  of  the  envelope  without 
rupturing  its  walls. 

For  mining  in  rock  or  coal,  blasting  powder  is  better  than 
cannon  powder,  since  the  end  sought  is  rather  the  rup- 
ture of  the  envelope  than  the  dispersion  of  the  fragments. 
Its  force  depends  on  the  great  specific  volume  of  the  gases 
generated  rather  than  upon  their  temperature. 

For  blasting  in  earth,  cannon  powder  is  better  than  blast- 
ing powder  as  its  potential  is  higher.  Its  diminished  den- 
sity, compared  to  high  explosives,  distributes  the  effect  over 
a  larger  area. 

MILITARY    EXPLOSIVES. 

The  principal  explosives  used  in  warfare  are  of  two 
general  classes: 

1.  Mixtures. 

Gunpowder  and  its  like;  these  are  more  or  less  inti- 
mate mechanical  mixtures  of  combustibles,  such  as  C,  S,  Sb, 
with  an  oxydizing  agent,  generally  a  nitrate  or  a  chlorate. 


10  ■       II. — EXPLOSIVE    AGENTS. 

Explosives  of  class  1  are  relatively  stable. 

2.  Compounds. 

Nitro-glycerine  and  gun-cotton  and  their  derivatives. 
These  are  chemical  compounds,  formed  by  the  substitution,  in 
an  organic  substance  of  the  general  form  C^  Hy  0„  of 
3  molecules  of  NO2  for  3  atoms  of  H. 

The  weak  affinity  of  N  renders  the  NO^  a  readily  acces- 
sible magazine  of  oxygen. 

Explosives  of  class  2  are  called  high  explosives,  and 
are  relatively  unstable.  In  this  class  are  included  the 
fulminatmg  compounds.     See  Chap.  XIV. 

GUNPOWDER. 

This  is  formed  of  a  mixture  of  KNO3;  C,  and  S,  in  the 
proportions  of  about  75,  15,  10.  These  proportions  are 
considerably  varied  in  pyrotechnic  compositions. 

The  conversion  of  gunpowder  is  approximately  expressed 
by  the  following  reaction: 

4KN03-|-Q  +  S=K2C03  +  K2S04  +  N,-i-2COa4-CO. 

The  reaction  is  really  much  more  complex,  and  varies 
with  the  circumstances  attending  the  explosion,  even 
though  great  care  be  taken  to  make  them  constant. 

Illustration. 

The  parts  played  by  the  three  ingredients  may  be  im- 
agined by  reference  to  the  forced  combustion  of  coal  in  a 
furnace. 

The  charcoal,  in  which  form  C  is  introduced,  forms  the 
main  supply  of  fuel.  The  sulphur,  owing  to  the  ease  with 
which  it  is  ignited,  takes  the  place  of  the  kindling  material. 
The  nitre  acts  as  a  bellows  forcing  in  air. 

The  sulphur  also  gives  coherence  to  the  grain,  correct- 
ing the  friability  of  a  binary  mixture  of  carbon  and  nitre. 


11. — EXPLOSIVE    AGENTS.  11 

Advantages  and  Disadvantages. 

The  facility  with  which,  by  varying  the  proportions  and 
the  arrangement  of  the  ingredients  of  gunpowder  its 
conversion  may  be  controlled,  and  also  its  comparative 
stability  against  accidental  ignition,  have  hitherto  com- 
pensated for  its  defects. 

These  refer  to  its  bulk,  the  care  required  in  storage,  its 
sensitiveness  to  dampness,  the  large  solid  residue  left  from 
its  conversion,  and  the  danger  attending  its  manufacture. 
While  for  special  purposes,  where  great  force  is  required,  it 
is  being  supplanted  by  the  high  explosives;  its  value,  as  a 
reservoir  of  potential  energy  for  purposes  of  propulsion, 
increases  as  our  knowledge  of  its  properties  extends. 

Note  to  page  7. 

1.  From  the  chemistry  we  have  p  v  =/o  ^^o  ( 1  H 7  =  — 7  ) .      If  in 

\        273       ^Tdl 

this  we  make  v  =  l,  then  by  definition  /=  p  =  — — ^ — -  =  — . 

•^      ^  273  273    C 


III. — INGREDIENTS   OF    GUNPOWDER. 


CHAPTER   III. 
INGREDIENTS  OF  GUNPOWDER. 

COMBUSTIBLES. 

1.  Sulphur* 
Preparation. 

This   is  refined  by  distillation.     The  product   is   called 
"flowers  of  sulphur,"  or  "rock  sulphur  "  or  "brimstone," 
according  to  the  temperature  at  which  the  volatile   pro- 
ducts are  condensed. 
Properties. 

If  below  115°,  minute  crystals  or  "flowers"  are  formed; 
above  that  temperature,  the  vapors  condense  in  a  liquid 
form,  which  is  cast  into  moulds.  Flowers  of  sulphur  are 
not  used  for  gunpowder,  as  they  contain  SOg  and  HgSOji 
which  are  hygroscopic. 

2.  Charcoal, 
Material. 

Charcoal  used  for  gunpowder  is  made  from  wood,  the 
composition  of  which,  excluding  water  and  ash,  is  repre- 
sented by  CeHioOg,  corresponding  to  the  following  propor- 
tions per  cent.: 


c, 

44 

H, 

6 

0. 

50 

100 

The  object  of  carbonizing  the  wood  is  twofold.     1st.  To 
increase  the  calorific  value  of  the  fuel  by  increasing  the 


III. — INGREDIENTS    OF    GUNPOWDER. 


proportion  of  carbon.     2d.  To  increase  its  calorific  inten- 
sity by  facilitating  its  reduction  to  powder. 
Composition. 

Gunpowder  charcoal  consists  of  from  55  to  85  per  cent, 
of  carbon  with  varying  proportions  of  hydrogen,  oxygen, 
and  ash.  Its  imperfect  distillation  leaves  varying  amounts  of 
hydro-carbons  which  increase  its  inflammabiUty,  and,  owing  to 
the  calorific  value  of  hydrogen,  may  increase  its  potential. 
Condition. 

The  uniform  action  of  fired  gunpowder  and  the  safety  of 
its  manufacture  depend  largely  upon  uniformity  in  the 
condition  of  the  principal  fuel  which  it  contains. 

Uniformity  is  sought  by  using  the  same  kind  of  wood, 
carbonized  by  the  same  process;  the  temperature  being 
raised  at  the  same  rate  to  a  point  which,  for  each  grade  of 
charcoal,  is  the  same. 

PREPARATION. 

Preliminaries. 

White  woods,  such  as  the  young  willow  or  alder,  which 
are  soft  and  of  rapid  growth,  are  preferably  employed, 
since  they  yield  a  charcoal  that  is  inflammable,  friable,  and 
free  from  ash. 

The  bark  is   removed,  so  as  to  facilitate  drying   in  the 
open  air,  and  to    free  the  coal  from  earthy  matter  and 
salts. 
Distillation. 

The  wood  is  usually  distilled  in  iron  retorts,  surrounded 
by  flame  consisting  largely  of  the  gases  evolved  by  the 
process:  Figures  1  and  2. 

For  convenience,  the  wood  is  charged  in  slips^  which  are 
cylinders  of  thin  sheet  iron. 

The  progress  of  the  operation  is  judged  of  by  test  sticks, 
withdrawn  from  time  to  time  for  examination;  by  the  use  of 


HI. — INGREDIENTS   OF   GUNPOWDER. 


a  pyrometer,  or  by  the  appearance  of  the  flame  and  smoke 
as  follows. 

Phenomena  of  Carbonization. 

The  rate  of  distillation  being  always  slow,  the  character- 
istics of  the  product  depend  principally  upon  the  temper- 
ature at  which  the  process  ceases.  Five  stages  are  recog- 
nized, of  which  three  correspond  to  useful  grades  of 
charcoal. 

I.  Up  to  150°,  desiccation  occurs. 

II.  At  150°,  decomposition  begins,  and  continues  as  fol- 
lows:— 

1st.      H  and  O  are  evolved  and  unite. 

2nd.  Three  acid  oxides  (carbonic,  acetic,  and 
pyroligneous  acids. — COg;  CH3,  CO2H;  CgH^Og) 
and  an  empyreumatic  oil  of  an  analogous  com- 
position are  evolved. 

3rd.     Soot  comes  forth  in  heavy  clouds. 

4th.     The  gases  burn  with  a  ruddy  flame. 

6th.  As  the  proportion  of  O  diminishes,  CO  re- 
places CO2,  and  at  260°,  the  flame  becomes  blue. 

The  solid  products  are  called  brands  (Fr.  fumer- 
ons)j  which  smoke  in  burning. 

III.  From  260°  to  270°,  brown  charcoal  is  formed.  It  is 
smokeless  but  tough. 

IV.  From  270°  to  340°  is  the  period  of  the  formation  of 
hydro-carbons;  both  gaseous,  viz.:  defiant  and  marsh  gases 
(Cg  H^;  C  HJ,  and  in  various  liquid  forms,  including  coal 
tar.  The  gases  burn  with  a  yellow  flame,  which,  as  the 
proportion  of  C  diminishes,  gradually  becomes  pale. 

At  280°  the  liberation  of  the  hydro-carbons  changes  the 
charcoal  from  brown  to  red  (charbon  roux);  it  tends  to 
raise  the  temperature  suddenly  to  about  340°. 


III. — INGREDIENTS   OF    GUNPOWDER. 


The  effect  of  this  rise  in  temperature  is  to  convert  the 
red  coal  to  the  next  grade,  which  is  black.  The  redness 
of  the  product  will,  therefore,  depend  upon  the  care  taken 
in  regulating  the  temperature.  This  is  done  by  drawing 
the  fire,  and  completing  the  process  by  the  residual  heat. 

The  operation  is  difficult  and  the  product  not  uniform. 

V.  Above  340°,  black  charcoal  is  formed  in  proportions 
increasing  with  the  temperature,  as  indicated  by  the  in- 
creasing whiteness  of  the  flame. 

The  effect  of  increasing  the  temperature  upon  the  pro- 
portions of  the  constituent  elements  is  shown  roughly  by 
the  following  table: 

Max.  Temperature..      150°      260°      280°      350° 

Prr»rln/^fo  Dried  Brown  Red  Black 

jrruUUCLb.  , Wood,  Coal.  Coal.  Coal. 

Carbon 44.0       68.0       71.0       77.0 

Hydrogen 6.0         5.0         4.5         4.0 

Oxygen 50.0       27.0       24.5       19.0 

Proportion  of  Weight 

of  Dried  Wood...    100.0  60  37         30 

Physical  Properties. 

The  physical  properties  also  change.  The  higher  the 
temperature — 

the  more —  the  less — 

1.  brittle;  1.  hygroscopic; 

2.  hard  and  dense ;  2.  violent  as  an  ingredient 

3.  prone  to  spontaneous  com-  of  gunpowder — 

bustion — 
does  charcoal  become. 

SPONTANEOUS    IGNITION   OF    CHARCOAL, 

Cause. 

The  property  of  charcoal  by  which  it  condenses  gases 
within  its  pores,  particularly  the  vapor  of  water,  may  raise 
its  temperature  to  the  point  of  ignition.     This  ^  facilitated 


in. — INGREDIENTS   OF    GUNPOWDER. 


by  the  occluded  oxygen  and  by  the  increased  surface  result- 
ing from  pulverization. 
Preservation. 

To  prevent  accident,  it  is  cooled  slowly,  and  kept  in  the 
stick  for  several  days.  To  obtain  uniformity  in  the  amount 
of  water  occluded,  it  is  prepared  only  as  required  for  use. 

Its  power  of  spontaneous  ignition,  when  pulverized,  is 
destroyed  by  mixing  it  with  sulphur  or  nitre. 

MANUFACTURE    OF    BROWN    CHARCOAL    BY    SUPERHEATED 
STEAM. 

Process. 

The  uniform  production  of  brown  charcoal  may  be 
accomplished  by  exposing  it  for  a  longer  period  to  a  some- 
what lower  temperature  than  that  above  assigned  as  the 
maximum.  For  this  purpose  superheated  steam  is  used,  as 
shown  in  figure  3. 
Eetort. 

The  retort  is  a  fixed  vertical  cylinder  of  boiler  iron, 
jacketed  with  mineral  cotton.  (Bloxam,  Art.  217.) 

Through  perforations  in  the  cast-iron  top  enters  a  cur- 
rent of  steam  which  has  been  superheated  in  a  coil  to  about 
230°. 

The  wood  is  piled  vertically  on  a  perforated  false  bottom 
made  fast  to  an  axial  bar,  by  which  the  contents  can  be 
removed. 

The  condensed  steam  and  the  water,  acids,  and  tar  drain 
through  the  pipe  shown. 
Product. 

The  process  lasts  about  four  hours,  being  stopped  when 
experience  shows  that  the  fibrous  structure  of  the  wood  is 
about  to  disappear. 

The  fiber,  which  is  retained  for  its  binding  effect  on  the 
structure  of  the  powder  made  from  this  coal,  notably 
increases  the  difficulty  of  pulverizing  it. 


III. — INGREDIENTS   OF    GUNPOWDER. 


OXYDIZING    AGENTS. 

1.  Nitre. 
Source. 

Only  about  one-tenth  of  the  supply  of  nitre  is  the  native 
Indian  product;  the  remainder  comes  from  the  double 
decomposition  of  the  sodium  nitrate  with  a  potassium  salt. 

Impurities. 

The  principal  impurities  are  the  chlorides,  the  affinity  of 
which  for  moisture  renders  them  objectionable.  Not  over 
■g-g^  is  allowed  in  nitre  used  for  government  gunpowder. 

2.  Sodium  Nitrate, 
Advantages. 

1.  It  is  cheaper  than  nitre  for  equal  weights. 

2.  Owing  to  the  relative  atomic  weights  of  sodium  (23), 
and  potassium  (39),  85  per  cent,  of  the. usual  proportion  of 
nitre  suffices  as  a  supply  of  oxygen,  still  further  reducing 
its  cost. 

3.  If  the  usual  proportion  of  75  per  cent,  be  retained,  the 
greater  volume  of  gas  evolved  increases  the  force  of  the 
powder  and  adapts  it  especially  for  blasting. 

Disadvantages. 

1.  The  deliquescent  properties  attributed  to  the  salt  are 
detrimental  when  the  powder  made  from  it  is  to  be  stored. 

2.  The  salt  is  more  soluble  than  nitre,  and,  therefore, 
powder  made  from  it  suffers  more  than  ordinary  powder 
from  the  segregation  of  the  salt  by  efflorescence.  This  is 
due  to  the  acqueous  vapor  condensed  in  the  pores  of  the 
charcoal  which  the  powder  contains.  When  the  powder  is 
made  on  the  spot  where  it  is  used,  as  in  the  excavation  of  the 
Suez  Canal,  this  objection  need  not  apply. 


III. INGREDIENTS    OF    GUNPOWDER. 


3.  Potassium  Chlorate. 
Disadvantages. 

1.  The  low  temperature  of  conversion,  due  to  the  affinity 
of  chlorine  for  the  metals,  renders  the  powder  dangerous 
when  exposed  to  shock. 

2.  Its  conversion  gives  free  chlorine,  which  attacks  the 
bore  of  the  gun  and  is  injurious  to  the  gunners. 

3.  It  is  costly. 

4.  The  uncontrollable  violence  of  mixtures  containing 
the  chlorates  relegates  them  to  the  category  of  the  high 
explosives  discussed  in  Chap.  XIV. 

They  are  principally  iemployed  for  igniting  other  explo* 
5ives;  themselves  being  ignited  by  friction. 

4.  Ammonium  Nitrate, 

This  is  becoming  extensively  used  in  the  so-called  smoke- 
less powders  for  heavy  cannon. 

Advantages. 

The  products  of  combustion  are  gaseous  or  volatile,  so 
that  the  smoke  is  greatly  diminished  in  density,  and  the 
entire  volume  occupied  by  the  powder  is  available  for  the 
expansion  of  the  gases. 

Disadvantages. 

The  deliquescence  of  this  salt  requires  that  powder  made 
from  it  be  hermetically  sealed.  This  prevents  the  use  of 
the  ordinary  cartridge  bags. 


IV. THE  MANUFACTURE  OF  GUNPOWDER. 


CHAPTER  IV. 

THE  MANUFACTURE  OF  GUNPOWDER. 


ACCIDENTS. 

Buildings. 

Owing  to  the  danger  of  explosion  the  buildings  are  scat- 
tered as  much  as  possible  and  are  separated  by  traverses  or 
rows  of  trees.     Figs.  1,  2. 

The  buildings  are  generally  constructed  with  heavy  walls 
on  three  sides,  the  remaining  side  and  the  roof  being  as 
light  as  practicable,  so  as  not  to  increase  the  violence  of 
explosions  by  unnecessary  confinement.     Fig.  3. 

Power. 

The  machines  employed  are  usually  automatic,  power  being 
conveyed  by  canals  (fig.  1),  or  wire  rope  (fig.  2),  radiating 
from  a  central  steam  engine.  As  a  general  rule  safety  is 
enhanced  by  slowly  operating  the  machines. 

Precautions. 

The  machines  are  started  and  stopped  from  an  outside 
shelter,  the  completion  of  the  operation  being  indicated  by 
an  automatic  signal.  Great  care  is  taken  to  prevent  the  in- 
troduction of  foreign  matter,  the  workmen  being  required 
to  change  their  clothing  before  entering,  and  wearing  rubber 
overshoes  within  the  buildings,  at  the  door  of  each  of  which 
is  a  wet  mat. 

All  parts  of  the  machines  liable  to  become  loose  are  boxed 
in.  Iron  is  replaced,  wherever  possible,  by  gun-metal,  copper, 
or  wood. 


IV. — THE  MANUFACTURE  OP  GUNPOWDER. 


Automatic  devices  are  arranged  to  drench  the  contents  of 
buildings  adjacent  to  a  probable  explosion. 

The  diffusion  of  dust  is  avoided  by  boxing  in  those 
machines  which  produce  it. 

Powder  in  barrels  is  always  gently  handled.  It  should 
never  be  rolled  for  transportation. 

These  details  are  given  to  suggest  the  precautions  neces- 
sary while  handling  gunpowder  in  service. 

PRINCIPLES   OF     THE    MACHINES    EMPLOYED   IN    THE   MANU- 
FACTURE   OF     GUNPOWDER. 

Types. 

In  order  to  derive  the  benefits  of  continuous  operation, 
the  tools yOX  portions  of  the  machines  in  contact  with  the 
material,  are  preferably  of  the  rotary  type.  Reciprocating 
motion  is  objectionable,  in  that  it  wastes  energy  in  revers- 
ing the  direction  of  the  motion  at  each  end  of  the  stroke. 

Classification. — The  tools  employed  may  be  classified  ac- 
cording to  their  functions,  as  follows: 


FUNCTIONS. 

NAME   OP  TOOLS. 

Nature 

of 
Operation. 

General. 

Special. 

General.         Special. 

U.B011S     \l^ 

continuous. 

fl.  disintegration 

intermittent. 

{ 2.  Barrels        tumblins 

contnmous. 

1. 

To  divide  by 

. 

fl.  cylindrical 

continuous. 

1 2.  separation 

Sieves    ■ 

2.  flat 

1 

intermittent  by 
reciprocating 
motion. 

fl.  mixinff 

Batrels        tumbling 

continuous. 

n. 

To  combine  by-j 

L2.  pressure 

fl.  rolling 
Th'^sjifin  \  2-  thrusting 
Pi  esses  \      (hydraulic) 

continuous, 
intermittent  by 
reciprocating 

motion. 

ni. 

To  convey  by 

Bands         endless 

continuous. 

The   rotary  tools   may  be  classified  as  to  whether  the 
material  lies  without  or  within  the  tool;  as — 
1st.  Rolls. 
2d.  Tumbling  or  rolling  barrels. 


IV. — TME   MANU^ACTtrkE   OF   CtJNfOWDEft. 


Rolls. 

The  object  of  a  roller  or  roll  is  twofold. 

1st.  To  concentrate  a  given  pressure  on  a  small  area  of 
contact. 

2nd.  To  transfer  this  pressure  to  successive  areas  contin- 
uously. 

Relative  motion  between  the  material  and  the  tool  is,  there- 
fore, necessary. 
Eeduction  of  Area. 

The  reduction  of  area  desired  is  generally  attained  by 
the  curvature  given  to  the  smooth  cylindrical  surface  of  the 
roll;  it  may  be  increased  by  fluting  the  surface  or  by  provid- 
ing it  with  pyramidal  points. 

The  effect  upon  a  granular  material  then  resembles  crack- 
ing, rather  than  the  crushing  effect  of  the  smooth  roller. 
Transfer  of  Pressure. 

When  the  pressure  is  transferred  but  slowly,  the  parti- 
cles of  the  material  may  have  time  to  adjust  themselves  in 
their  new  positions.  The  effect  of  the  pressure  will  then  be 
rather  to  condense  the  material  than  to  disintegrate  it  by 
crushing. 
Eelative  Motion. 

1.  When  the  material  is  at  rest,  a  single  roller  is  used. 
Example:  a  rolling-pin.     See  fig.  8. 

In  practice,  the  path  of  the  roller  is  circular,  so  that  its 
effects  may  be  repeated. 

2.  When  the  material  moves,  the  rollers  are  in  pairs  and 
revolve  on  fixed  axes  in  relatively  opposite  directions.  Ex- 
ample: A  clothes  wringer.     See  fig.  14. 

In  this  case,  they  act  but  once  upon  the  material,  which  is 
carried  through  them  by  friction,  and  fed  to  and  removed 
from  the  rollers  by  its  weight. 

To  assist  in  feeding  automatically,  several  pairs  of  rollers 
may  be  placed  in  tiers,  surmounted  by  a  hopper  containing 


4  IV. — The  manufacture  op  gunpowder. 

the  material  to  be  disintegrated.  The  upper  tiers  have  the 
coarsest  teeth  and  are  placed  farthest  apart. 

A  coffee-mill  is  a  variety  of  this  class.  The  rolls  are  ver- 
tical, concentric,  and  conical; the  outer  roll,  which  is  fixed, 
being  the  more  obtuse.  The  funnel-shaped  space  between 
them  serves  as  a  hopper,  and  as  the  material  descends,  pro- 
duces the  effect  obtained  by  the  successive  tiers  above  de- 
scribed. 

Fig.  4  shows  a  charcoal-mill  and  sieve.  The  roll  is  bal- 
anced to  avoid  excessive  pressure. 

Barrels, 
Type. 

Tumbling  barrels,  as  represented  in  fig.  5,  are  much  used 
in  the  arts  for  abrasion.  Their  utility  depends  upon  the 
inter-attrition  of  the  contents.  In  powder  making,  besides 
the  material,  these  often  consist  of  balls,  b,  b,  lifted  by  ledges, 
Z,  Z,  and  continually  falling  back  upon  the  material  beneath 
them. 

When  the  operation  has  proceeded  far  enough,  the  door 
JD  is  removed,  disclosing  a  perforated  screen  through  which 
the  finer  portions  may  gradually  escape  upon  the  oscillating 
sieve,  S. 

The  product  is  collected  in  the  drawer  Z>/ 

Varieties. 

The  nature  of  the  barrel  and  of  the  balls  varies  with  the 
explosiveness  of  the  material  and  the  character  of  the 
operation.  Thus,  the  barrel  may  be  of  iron  with  iron  balls 
where  an  inexplosive  material  is  to  be  pulverized*;  of  a 
wooden  skeleton  covered  with  leather,  using  bronze  or  zinc 
balls,  when  the  operation  is  dangerous;  or  covered  with  wire 


*When   the   material  to  be  disintegrated  is  very  tough,  heavy  iron 
cylinders  are  used  instead  of  balls. 


IV. — THE  MANUFACTURE  OF  GUNPOWDER.       0 

gauze  netting,  and  using  wooden  balls,  where  simple  com- 
minution of  a  friable  material  is  desired. 

By  omitting  the  balls  and  varying  the  size  of  the  netting, 
such  barrels  may  be  used  as  sieves;  and,  by  slightly  inclining 
their  axes  to  the  horizon,  both  ends  may  be  left  open,  when 
they  will  remove  the  dust.     Fig.  4. 

If  the  barrels  be  tight  and  no  balls  be  used,  the  contents 
will  be  merely  polished.  Such  tools  are  much  used  in  the 
arts  for  finishing  the  surface  of  rough  metallic  objects,  and, 
in  the  manufacture  of  gunpowder,  for  glazing  it. 

Mixing  Barrels. 

Where  simple  mixture  of  the  ingredients  'is  sought,  the 
barrel  may  contain  paddles  revolving  independently  upon 
its  axle,  as  in  a  churn,  fig.  6.  The  action  of  these  paddles 
is  also  disintegrating,  and,  where  time  is  important,  may 
replace  the  more  crude  pulverizing  apparatus  described. 
Advantages. 

The  principal  advantage  of  the  rolling  barrels  consists  in 
their  cheapness  of  construction  and  operation,  by  which 
their  number  may  be  multiplied,  and  the  eifects  of  an 
explosion  diminished. 

Carrying  Bands. 

These  are  endless  belts  of  a  suitable  width,  which  serve 
to  carry  continuously  the  material  from  one  part  of  a 
machine  to  another. 

If  horizontal,  a  plain  band  will  suffice;  but,  if  inclined,  it 
is  furnished  with  elevator  buckets.     Fig.  7. 

OPERATIONS   OF   MANUFACTURE. 

Processes, 
Nature. 

All  the  stages  of  manufacture  may  be  referred  to  the 
following  essential  processes. 


b  IV. — THE   MANUFACTURE    OF    GUNPOWDER. 

1.  Formation  of  a  homogeneous  press  cake  of  required 
density. 

2.  Breaking  up  the  press  cake  into  grains  of  required 
size  and  form. 

3.  Finishing  the  grains  so  formed. 

Operations. 

The    necessary    operations    may  be   divided   into   four 
principal  groups,  viz.: 

Jl.  Pulverizing. 
2.  Mixing. 
3.  Moistening. 

II.  Operations  relating  to  press  cake.  ]  \  p"ressi^n°^^^^"^' 
III.  Operations  relating  to  graining,      -j  \;  gjf^/^^"^ 


IV.   Operations  relating  to  finishing. 


'1.  Glazing. 

2.  Drying. 

3.  Dusting. 

4.  Blending. 

5.  Marking. 


X  PRELIMINARY   OPERATIONS. 

1.  Pulverizing, 
Process. 

The  nitre  is  generally  in  crystals  that  are  sufficiently 
fine.  Otherwise,  this  and  the  other  materials  are  pulverized 
by  any  suitable  process,  either  separately  under  single  rolls 
or  by  a  binary  process  in  a  barrel,  viz.:  the  charcoal  and 
sulphur  together,  or  the  charcoal  and  nitre  together. 

Object. 

The  pulverization  should  be  thorough,  so  as  to  reduce 
the  time  required  for  incorporation  ;  the  latter,  owing  to  the 
cost  of  the  plant  and  the  smallness  of  the  "  charges  "  treated, 
is  the  most  expensive  of  the  operations. 


IV. — THE    MANUFACTURE    OF    GUNPOWDER.  7 

2.  Mixiftg. 

The  three  ingredients  may  be  mixed  by  hand  or  in  the 
rolling  barrel. 

3.  Moistening. 
Object. 

The  object  of  moistening  is  generally  to  assist  in  the 
distribution  of  the  nitre;  to  give  consistency  to  the  mass; 
and  to  prevent  a  dangerous  rise  in  temperature  during  the 
various  operations  of  manufacture. 

Limits. 

An  excess  of  moisture  may  cause  segregation  of  the 
nitre  by  crystallization,  and  its  evaporation,  as  in  store,  may 
render  the  finished  powder  unduly  porous. 

On  the  other  hand,  extreme  desiccation  may  lead  to  the 
re-absorption  of  hygrometric  moisture,  which  would  affect 
the  properties  of  the  powder  dried. 

The  amount  of  moisture  should  never  exceed  3  or  4  per 
cent.  It  is  frequently  renewed  during  manufacture,  accord- 
ing to  the  state  of  the  atmosphere  and  to  the  special  object 
in  view.  The  amount  present  is  determined  by  desiccating 
a  weighed  sample. 

II.    OPERATIONS   RELATING    TO    PRESS   CAKE. 

1.  Incorporating. 
Object. 

This  is  intended  to  unite  the  dust  of  the  ingredients  as 
intimately  as  mechanical  means  permit,  and  thereby  to  facili- 
tate the  conversion  of  the  powder  into  gas.  It  is  the  most 
important  of  all  the  operations  of  manufacture. 

Process. 

The  wheel  mill  (Figs.  8  and  9),  used  for  this  purpose,  con- 
sists of  two  cast-iron  cylinders  Cy  c^  weighing  several  tons 
each  and  acting  as  single  rolls. 


b  IV. — THE  MANUFACTURE  OF  GUNPOWDER. 

In  order  that  their  effect  may  be  exerted  throughout  the 
layer  of  composition,  this  is  made  only  about  one  inch  thick. 

The  risk  attending  this  disposition  is  diminished  by  fre- 
quent careful  moistening,  and  by  the  eccentricity  of  the  axle; 
this  permits  the  wheels  to  rise  and  fall  as  obstacles  are 
encountered.  The  constancy  of  the  resulting  pressure  in- 
creases the  uniformity  of  their  effect.  This  arrangement  is 
shown  in  Fig.  9. 

The  arrangement  of  the  wheels  upon  an  axis  rotating  in 
a  horizontal  plane  peculiarly  adapts  them  to  the  require- 
ments of  this  operation.  For,  while  both  edges  of  either 
wheel  have  the  same  angular  velocity,  their  paths  described 
in  the  same  time  are  notably  different.  Hence,  it  follows 
that  the  inner  ed^e  will  tend  to  slide  backward  relatively  to 
the  outer  edge;  giving  to  the  wheel  a  motion  of  rotation 
about  an  instantaneous  vertical  axis,  combined  with  that 
about  its  permanent  horizontal  axis. 

The  effect  is  to  grind  the  material  nearest  to  the  centre 
more  thoroughly  than  that  nearest  to  the  curb  of  the 
trough;  because  in  the  former  case,  the  sliding  of  the  wheel 
repeats  the  effect  of  its  crushing,  and,  in  the  latter  case 
replaces  it  in  part. 

This  effect  is  distributed  by  means  of  ploughs  preceding 
the  wheels,  and  by  causing  the  wheels  to  travel  in  different 
paths. 

The  process  takes  about  two  hours,  depending  on  the 
quality  of  the  product;  it  continues  day  and  night,  while 
that  of  the  other  machines  is  confined  to  daylight. 

Product. 

The  product  of  the  wheel  mill,  called  mi7/  cake,  unless 
consolidated  by  very  slow  rolling,  is  friable  and  of  variable 
thickness  and  density.  These  defects  are  corrected  by  the 
next  process. 

The  perfectness  of  the  incorporation  may  be  tested  by 


IV. — THE  MANUFACTURE  OF  GUNPOWDER.       9 

flashing  a  small  quantity  upon  a  glass  plate.     No  residue 
should  be  left.     The  stains  left  by  flashing  powder  on  the 
blue   paper   used  in  solar  printing  are  characteristic,  and 
increase  the  delicacy  of  the  test. 
Variations  in  Process. 

In  case  of  necessity  the  incorporation  may  be  less 
perfectly  performed  by  the  stamp  mill  (Fig.  13),  or  by  the 
protracted  use  of  the  rolling  barrel.     (See  also  page  15.) 

2.  Pressing, 
Object. 

The  object  of  pressing  powder  is  to  increase  its  density 
as  a  fuel,  and  to  give  it  sufficient  hardness  to  resist  the 
formation  of  dust  in  transportation. 
Kind  of  Press. 

The  intensity  and  uniformity  of  the  pressure  required 
usually  demand  the  action  of  an  hydraulic  press,  Fig.  10; 
although,  when  quantity   rather   than  quality   is  desired, 
single  or  double  rolls  may  be  employed. 
Process. 

To  increase  the  uniformity  of  the  material  pressed,  the 
product  of  the  various  wheel  mills  is  coarsely  granulated 
and  mixed.  Then,  having  been  moistened,  it  is  placed  in 
layers  between  plates  which  are  kept  at  about  two  inches 
apart  until  the  spaces  between  them  are  filled. 

The  powder  is  then  gradually  compressed  to  about  half 
its  former  volume;  being  kept  from  spreading  by  hinged 
side  pieces,  which,  being  latched  together,  form  a  sort  of 
box.  This  box  is  generally  vertical,  but  for  convenience  is^ 
preferably  horizontal  and  on  the  level  of  the  floor. 
Variations  in  Density. 

The  resulting  density  increases  within  limits,  with  the 
duration  of  the  pressure  and  with  the  amount  of  trituration 
which  the  powder  has  received.     The  proportion  of  mois- 


10      IV. — THE  MANUFACTURE  OF  GUNPOWDER. 

ture  largely  affects  the  density,  since  it  acts  as  a  lubricant 
between  the  particles.  The  density  is  not  uniform  through- 
out the  press  cake,  being  always  greatest  next  to  the  mov- 
ing surface. 

To  obtain  uniform  density,  upon  which  it  will  be  seen 
that  the  uniform  action  of  powder  greatly  depends,  one 
must  compress  equal  masses  equally  incorporated  and  con- 
taining equal  quantities  of  water  at  equal  rates  into  equal 
volumes. 

Wiener's  Powder. 

These  requisites  are  with  difficulty  attained,  owing  to  the 
variable  hygrometric  condition  of  the  atmosphere.  It  has 
been  attempted  to  dispense  with  water  for  pressing,  by 
heating  the  powder  during  this  operation  slightly  above  the 
melting  point  of  sulphur. 

This  process,  invented  by  Colonel  Wiener,  of  Russia, 
renders  the  gunpowder  practically  waterproof. 

Effect  of  Form  of  Plates. 

The  plates  between  which  the  powder  is  pressed  are  gen- 
erally flat,  in  which  case  the  press  cake  comes  from  the  press 
in  slate-like  slabs.  The  powder,  resulting  from  breaking  up 
these  cakes,  is  called  of  irregular  granulation^  or  simply 
grained  powder. 

Modern  powders  for  heavy  guns  are  often  pressed  be- 
tween plates,  the  surfaces  of  which  are  regularly  indented 
or  ribbed  after  the  manner  of  a  waffle  iron  (Figs.  11,  12). 
The  resulting  press  cake  may  be  readily  broken  up  into 
grains  of  great  uniformity  of  size  and  shape.  Such  powders 
are  said  to  be  of  regular  granulation. 

Molded  Powder. 

When  the  press  cake  is  made  exceedingly  small,  so  that 
each  cake  shall  make  one  grain,  the  powder  is  said  to  be 
molded.     See  molded  J>rismatic,  Figure  12. 


IV. — THE  MANUFACTURE  OF  GUNPOWDER.       11 

Such  powders  are  made  by  a  number  of  properly  shaped 
punches  and  dies  simultaneously  operated.     Fig.  15,  post. 
Concrete  Powders. 

The  structural  homogeneity  of  the  product  depends 
much  upon  the  condition  of  the  material  compressed.  If 
the  soft  mill  cake,  above  referred  to,  be  replaced  by  that 
which  has  already  been  pressed  and  granulated,  a  co7icrete 
powder  is  produced;  the  fine  grains  composing  it  being 
cemented  together  by  the  pressure  into  a  mass,  the 
porosity  of  which  is  greatest  in  the  middle.  The  burning 
of  this  powder  is  notably  different  from  that  of  the  homo- 
geneous mass  generally  produced. 

OPERATIONS    RELATING    TO   GRAINING. 

Object. 

The  object  of  graining,  like  that  of  splitting  fire  wood,  is 
to  increase  the  initial  surface  of  combustion. 
Operations. 

The  press  cake  is  broken  up  by  a  series  of  rolls  (Fig.  14), 
and  sifted  between  limiting  sieves. 
Principle  of  Gauging. 

The  use  of  these  sieves  illustrates  a  principle  common  in 
manufactures;  this  principle  when  it  is  applied  tp  individual 
articles,  is  called  gauging. 

Assuming  that  no  two  objects  can  be  made  of  precisely 
the  same  size,  a  certain  tolerance  is  established  by  the 
adoption  of  a  maximum  gauge,  through  which  each  object 
must  pass,  and  of  a  minimum  gauge,  through  which  no  ob- 
ject may  pass. 

The  grains  which  are  too  coarse  or  too  fine  are  reworked. 

Special  Operations  in    Graining, 

Regular  Granulation. 

These   depend   upon   the  kind   of  grain  required.      For 


13      IV. — THE  MANUFACTURE  OF  GUNPOWDER. 

example,  the  powders  of  regular  granulation  require  only 
breaking  up  as  by  hand. 
Pebble  Powder. 

The  English  cubical,  or  pebble  powder  is  made  by  cutting 
the  flat  press  cake  into  prisms  between  ribbed  rolls,  and 
then  recutting  these  prisms  across  their  length. 
Flat  Powder. 

The  flat  French  powder  (Castan's)  is  made  by  roughly 
breaking  a  rather  thin  press  cake,  so  as  to  make  the  thick- 
ness of  the  cake  the  minimum  dimension  of  the  finished 
grain.     (Fi^.  12.) 

IV. — OPERATIONS   RELATING    TO    FINISHING, 

1.  Glazing, 
Object. 

The  object  of  glazing  is  to  remove  the  angles  and  asper- 
ities of  the  grain;  these  would  form  dust  in  transportation 
and  facilitate  the  absorption  of  moisture  in  store. 

It  compensates  for  the  diminished  density  of  the  interior 
of  the  press  cake  from  which  most  of  the  grains  are  formed, 
by  increasing  their  superficial  density  by  their  mutual  col- 
lision; it  also  increases  the  homogeneity  of  their  struc- 
ture by  the  heat  which  is  thus  evolved. 
Process. 

Moisture  having  been  added  to  give  some  plasticity,  the 
grains  are  rolled  in  a  wooden  barrel  without  balls. 

2.  Drying, 
Object. 

The  object  of  drying  is  to  reduce  to  normal  limits,  the 
moisture  required  in  the  previous  stages  of  manufacture. 
Process. 

It  is  accomplished  by  passing  a  current  of  warm,  dry  air 
through  successive  layers'of  powder  spread  on  screens  or 
on  shallow  trays. 


IV. — THE  MANUFACTURE  OF  GUNPOWDER.      13 

The  temperature  should  be  increased  gradually,  to  avoid 
disintegration  of  the  grains. 

3.  Dustiftg, 
Object. 

This  is  intended  to  remove  the  dust  resulting  from  the 
glazing,  and  detached  from  the  surface  of  the  grains  by 
drying. 

4.  Blending, 
Object. 

To   neutralize   unavoidable   variations   in   manufacture, 
powders  of  the  same  size  and  nature  may  be  blended  so  as 
to  give  certain  average  results. 
Process. 

Fine  grain  powders  are  mixed  according  to  their  densi- 
ties, and  those  of  larger  grain,  according  to  their  ballistic 
properties.  Molded  powders  are  blended  in  charges,  grain 
by  grain  alternately. 

6.  Marking, 
In  the  U.  S.,  powders  receive  certain  conventional  fac- 
tory marks,  of  which  the  first  two  letters  generally  relate  to 
the  size  and  use,  and  the  final  letters  to  recorded  variations 
in  the  manufacture,  or  to  the  date  at  which  certain  lots  are 
made.  Thus,  I.  K.  A.  might  mean  the  first  lot  of  I.  K. 
powder  used  for  field  guns;  E.  V.  B.  the  second  lot  of 
hexagonal  powder  for  sea-coast  guns,  etc.  Similar  symbols 
are  used  abroad  and  are  very  convenient. 

VARIATIONS  IN  MANUFACTURE. 

COCOA    POWDER. 

History. 

The  most  important  improvement  in  gunpowder,  since 
1860,  is  the  invention  by  the  Germans  of  what,  from  its 
color,  is  called  cocoa  or  brown  powder. 


14  IV. — THE    MANUFACTURE    OF    GUNPOWDER. 

It  is  notable  for  being  the  first  important  modification  of 
the  long  established  composition  of  gunpowder  which  has 
proved  practically  successful,  and,  as  will  be  seen,  for  the 
paradoxical  nature  of  its  results.  In  this  country  it  has  so 
far  been  used  only  in  heavy  cannon. 

Characteristics. 

As  made  in  this  country  by  the  Du  Pont  Powder  Works, 
it  differs  from  ordinary  powder; — 

1.  In  the  composition  of  the  charcoal,  which  is  made  by 
steam  heat,  as  described  Chap.  III. 

2.  In  the  addition  during  incorporation  of  gummy  carbo- 
hydrates, such  as  sugar,  dextrine,  etc. 

3.  In  the  proportion  of  the  ingredients — 

Nitre,  81.5  per  cent. 

Charcoal  and  Carbo-Hydrates,   15.5 
Sulphur,  3. 

lOOO" 

4.  It  is  difficult  to  ignite,  requiring  in  the  gun  a  few 
prisms  of  black  powder  to  be  built  into  the  cartridge  near 
the  mouth  of  the  vent. 

6.  When  ignited,  unconfined,  it  seems  to/j/j^^rather  than 
to  deflagrate  explosively. 

This  and  its  want  of  friability  make  it  safe  to  transport 
and  handle  in  store. 

6.  It  is  quite  hygroscopic,  but  suffers  less  from  moisture 
than  black  powder. 

7.  Its  ballistic  properties  are  extraordinary, 

8.  It  gives  comparatively  little  smoke. 

Manufacture. 

This  resembles  that  of  all  the  molded  concrete  powders. 
The  grams  compressed  are  of  the  size  of  mortar  powder, 
and  are  slightly  moistened  before  pressing. 


TV. — THE  MANUFACTURE  OF  GUNPOWDER.      15 

Press  for  Molded  Powders. 

Pressing  is  done  by  carefully  regulating  the  motion  of  the 
plungers  of  a  duplex  hydraulic  press,  which  molds  about 
100  prisms  at  a  time. 

In  fig.  15,  ^  is  a  fixed  mold  plate  containing  a  number  of 
apertures  of  a  cylindrical  or  prismatic  form,  into  which  the 
perforated  plungers,  G^  Z,  fit. 

Through  the  axes  of  the  plungers  run  needles,  H,  sim- 
ultaneously operated  by  the  toggle-joint,  /,  and  the  supple- 
mentary cylinder,  K. 

A  quantity  of  powder  is  swept  into  the  apertures,  X^  until 
they,  are  full.  The  rams,  B^  B' ,  then  approach  each  other 
with  equal  velocities;  and  as  L  enters  E,  ZT rises  into  L. 

After  suitable  pressure,  L  rises;  ZT  is  withdrawn,  and  G 
rises;  lifting  the  prism  so  that  it  may  be  swept  off  into  a 
box. 

The  resulting  prism  has  very  dense  ends,  separated  by  a 
somewhat  porous  belt. 

NORDENFELDT    POWDER. 

Object. 

To  increase  the  intimacy  of  the  incorporation  and  to 
avoid  the  danger  of  performing  it  by  mechanical  means. 

Manufacture. 
Charcoal. 

Straw  or   cotton-wool   is  carbonized   by   exposure  to  a 
stream  of  gaseous  HCl. 
Sulphur. 

Dissolved  in  CS^  and  added  to  Charcoal. 
Nitre. 

In  aqueous  solution  is  gradually  added  to  above. 

The  mass  is  mixed  by  paddles  while  in  a  liquid  state, 
after  which  the  vehicles  are  distilled  and  evaporated.  The 
usual  operations  following  incorporation  are  then  pursued. 


V. — INTERIOR    BALLISTICS. 


CHAPTER  V. 


INTERIOR    BALLISTICS. 

Division  of  Ballistics. 

Ballistics,  which  treats   of  the  motion  of  projectiles,  is 
divided  into  interior  and  exterior  ballistics,  according  as 
the  motion  of  the  projectile  within  or  without  the  gun  is 
considered. 
Interior  Ballistics. 

The  latter  science  is  studied  later  in  the  course;  but  the 
former  is  so  intimately  related  to  the  conversion  of  gun- 
powder into  gas,  that  it  is  expedient  to  deal  with  it  while 
the  circumstances  of  this  conversion  are  fresh  in  our  minds. 
The  Gun  as  a  Machine. 

Functionally  speaking,  the  gun  is  a  machine  by  which  the 
potential  energy  of  the  gunpowder  is  converted  into  the 
kinetic  energy  of  the  projectile. 

It  is  well  to  consider  in  advance  certain  elementary  prin- 
ciples relating  to  the  construction  of  this  machine  and  to 
the  measurement  of  the  energies  received  and  usefully 
converted. 

FORM    OF    GUN. 

strength  vs.  Weight  of  Guns. 
It  will  hereafter  appear  that, 
considering  a  gun  to  be  com- 
posed of  a  series  of  elementary 
concentric  cylinders,  the  resist- 
ance which  each  of  these  cylin- 
ders offers  to  a  permanent  tan- 
gential deformation  varies  in- 
versely with  the  square  of  its 
radius;  or,  if  S  represent  the 
stress,  ABy  on  the  interior  cir- 


tJ^IVE 


"\ 


O^' 


.-f*\ 


V. — INTERIOR   BALLISTICS. 


cumference  of  an  elementary  area  of  cross   section  of  the 
bore,  the  radius  of  which  is  r  j  and  y  be  the  stress  from  the 

same  cause  at  any  other  radius,  x;  then  j*  = — ^ .    This  is  ex- 

00 

pressed  by  figure  1. 

But  the  weight  of  the  elementary  longitudinal  cylinders 
increases  with  the  square  of  their  radii. 

It  therefore  appears,  that  after  a  certain  point,  an  increase 
in  the  thickness  of  the  walls  of  the  gun  adds  rapidly  to  its 
weight  and  but  slowly  to  its  strength. 

Strength  vs.  Cost. 

Also,  when  the  diameters  of  cannon  exceed  a  certain 
limit,  the  difficulties  of  construction  attending  an  increase 
in  diameter,  increase  much  more  rapidly  than  do  those  at- 
tending an  increase  in  length. 

Conclusion  as  to  Form  of  Gun. 

A  given  amount  of  energy  may,  therefore,  be  most 
economically  transferred  from  the  gunpowder  to  the  pro- 
jectile, by  diminishing  the  rate  of  transfer  and  increasing 
its  duration. 

Considerations  relating  to  the  weight  and  cost  of  a  given 
cannon  having  thus  determined  the  most  suitable  diameter, 
it  should  be  kept  constant  for  the  entire  length  of  the  gun, 
provided  that  the  stress  to  which  it  is  exposed  shall  also  be 
constant. 

It  is  the  object  of  recent  improvements  in  guns,  powder, 
and  projectiles,  to  make  this  stress  as  high  as  it  is  safe,  and 
to  prolong  it  as  far  as  possible  throughout  the  length  of  the 
bore. 

Recent  changes  in  the  profile  of  cannon  illustrate  the 
progress  which  has  so  far  been  attained  toward  realizing  the 
conditions  of  this  ideal  gun. 


-INTERIOR   BALLISTICS. 


FORM    OF   PROJECTILE. 

Until  quite  recently,  all  but  experimental  cannon  were 
muzzle  loaders. 

Until  about  1860,  they  were  smooth-bores  and  fired 
spherical  balls. 

The  success  of  the  rifled  field  pieces  in  the  war  between 
France  and  Austria  led  to  the  general  use  of  projectiles, 
oblong  in  shape,  but,  like  the  spherical  projectiles,  smaller 
than  the  bore. 

These  cannon  have  been  recently  replaced  by  rifled 
breech  loaders,  firing  projectiles  provided  with  a  compres- 
sible ring  slightly  greater  in  diameter  than  the  bore. 

The  enlarged  chamber,  which  this  form  of  projectile  re- 
quires, and  the  resistance  which  it  offers  to  motion,  consid- 
erably modify  the  circumstances  of  the  conversion. 


Note. — This  chapter  is  introductory  to  the  seven  following  chapters. 


VI. — VELOCIMETERS. 


CHAPTER  VI. 

VELOCIMETERS. 

Object. — In  order  to  study  experimentally  the  transfor- 
mation of  energy  from  the  gunpowder  to  the  projectile  and 
to  the  gun  and  carriage,  and  to  measure  the  kinetic  energy 
residing  in  the  projectile,  both  as  it  leaves  the  gun  and  when 
it  has  done  work  upon  the  medium  through  which  it  passes, 
special  instruments,  known  as  velocimeters^  chronographs^ 
chronoscopes,  etc.,  have  been  devised. 

Importance. — Except  where  otherwise  specified,  the  fol- 
lowing discussion  relates  to  the  means  employed  for  meas- 
uring the  initial  velocity  of  the  projectile.  This  is  the  great 
measure  upon  which  all  ballistic  predictions  are  based. 

Constituent  Parts. — All  such  instruments  are  chronometers 
and  consist  essentially  of  a  register  and  a  marker. 

The  register  has  a  known  velocity  relative  to  that  of  the 
marker  and  receives  from  it  a  succession  of  marks,  the 
time  equivalents  of  the  spaces  between  which  measure  the 
periods  between  certain  events. 

The  events  are  the  first  visible  effects  produced  upon  the 
velocimeter  by  the  arrival  of  the  projectile  at  certain 
epochal  points.     These  are  often  targets. 

Signal  Time. — The  interval  between  an  epoch  and  the 
corresponding  event  is  called  the  time  of  transmission,  or 
the  signal  time.   See  figure  14. 

The  time  from  any  origin  to  an  event  =  time  to  the 
epoch,  /,  +  signal  time,  G\  and  the  interval  between  two 
events,  8  =(/"  +  a")  -  {t'  +  6')^{t"  -f)  +  (a'  -  c').  If 
G''-a'=Oj  t'-t',  or  r,  =d.  If  a"-a'=Cj  r=d-C;  if 
•then  r=0,  d--C.  To  diminish  accidental  variations  in  C, 
a  is  made  as  small  as  possible.  Knowing  s,  the  distance 
between  the  epochal  points,  and  r,  the  mean  velocity  of  the 
projectile  over  the  intervening  path  may  be  determined. 


VI. VELOCIMETERS. 


Functions  of  Velocimeters. — Conceiving  times  and  dis- 
tances as  being  each  measured  from  common  origins,  we 
may  say  that  the  instruments  record  differences  in  instru- 
mental distance  corresponding  to  differences  in  time, 
which  differences  in  time  correspond  to  differences  in  dis- 
tance of  the  projectile  from  any  point  upon  its  trajectory. 

Classification. — The  velocimeters  may  be  divided  into 
three  general  classes  according  as  they  are  adapted  to 
record: — 

I.  One  difference  in  time  corresponding  to  one  definite 
difference  of  distance  of  the  projectile  from  a  common 
origin. 

II.  Successive  differences  in  time  corresponding  to  sev- 
eral successive  definite  differences  of  distance  of  the  pro- 
jectile from  a  common  origin. 

III.  Continuous  differences  in  time  corresponding  to  con- 
tinuous differences  of  distance  of  the  projectile  from  a  com- 
mon origin. 

Comparison  of  Classes. — For  each  fire  the  instruments  of 
class  I  determine  the  mean  velocity  of  the  projectile  between 
one  pair  of  points. 

Those  of  class  II  determine  that  between  several  succes- 
sive pairs  of  points. 

Those  of  class  III  set  forth  continuously  the  circumstances 
of  the  motion. 

By  taking  the  epochal  points  at  constant  intervals,  either 
of  distance  or  of  time,  the  indications  of  the  instruments  of 
class  II  may,  by  interpolation,  serve  to  determine  the  varia- 
tions in  velocity  corresponding  to  known  values  of  A  J  or  A  r 
and  thus  to  approximate  to  the  law  of  motion  more  fully 
expressed  by  the  record  of  instruments  of  class  III. 

This  method  enables  the  epochal  points  to  be  separated 
further  than  the  construction  of  the  instruments  of  class  III 
permits. 


VI. — VELOCIMETERS. 


CLASS  I. 

Events.— In  class  I  the  events  are  those  of  the  falling  of 
certain  masses,  either  freely  or  with  constrained  motion. 

The  position  of  the  marks  indicates  indirectly  the  interval 
of  time  separating  the  events. 

Operation. — Calling  the  masses  respectively  a  and  b,  ac- 
cording to  their  priority  of  fall,  b  is  caused  to  strike  a  while 
a  is  falling.  The  problem  resolves  itself  into  determining 
the  difference  between  two  intervals  of  time,  viz.: 

4=how  long  a  was  falling  before  it  was  struck. 

/b=how  long  it  took  b  to  strike  a. 

Then  4— 4=0=time  that  a  was  falling  before  b  started 
to  strike  it=:the  interval  between  the  starting  of  a  and  of  b^ 
which  is  the  time  interval  required. 

a  and  b  are  generally  caused  to  fall  by  the  demagnetiza- 
tion of  electro-magnets  in  separate  circuits,  which  are  broken 
by  the  arrival  of  the  projectile  at  the  epochal  points.  Or 
they  may  be  made  to  fall  by  the  cutting  of  taut  threads  by 
which  they  have  been  suspended. 

Disjunctor. — An  essential  appendage  to  machines  of  this 
class  is  the  disjunctor^  by  means  of  which, both  circuits  being 
simultaneously  broken,  the  masses  a  and  b  are  caused  sim- 
ultaneously to  fall. 

EXAMPLES    OF    CLASS   I. 

1.  THE  BENTON  VELOCIMETER. 

See  figures  1,  2  and  3. 

Description.— This  instrument,  devised  by  the  late  Colo- 
nel J.  G.  Benton,  the  first  Instructor  of  Ordnance  and  Gun- 
nery at  the  U.  S.  Military  Academy,  employs  either  elec- 
tricity or  threads  to  support  a  and  b.  These  are  similar 
pendulums  suspended  at  the  centre  d  of  the  arc  b  c  0  a  so 
that  they  are  constrained  to  oscillate  in  adjacent  planes  par- 
allel and  close  to  the  face  of  the  arc;  this  arc,  being  gradu- 
ated, forms  the  register. 


VI. VELOCIMETERS. 


That  pendulum  which  lies  nearest  to  the  arc  carries  at  its 
outer  end  the  marker;  this  is  a  delicate  bent  lever  pivoting 
in  a  plane  perpendicular  to  the  arc,  and  so  placed  that  its 
inner  end,  which  is  lightly  covered  with  printing  ink,  shall 
travel  close  to  the  register. 

As  the  pendulums  pass  each  other,  a  projection  on  tb.e 
inner  face  of  the  outer  pendulum  strikes  the  outer  end  of 
the  marker  and  causes  it  to  indicate  the  point  of  meeting  as 
at  c^  figure  2. 

Inspection  of  the  figure  shows  0=4 — 4=time  of  passage 
over  the  arc  a  o  c^  minus  time  of  passage  over  the  arc  b  ^:=2X 
time  of  passage  over  the  arc  o  c. 

Disjunctor. — The  disjunctor  in  this  instrument  serves  to 
determine  C,  the  difference  in  signal  times. 

It  consists  of  two  flat  steel  blades,  mn,  ni'n',  secured  to 
the  base  at  m^  7n' ^  and  having  their  free  ends,  n^  «',  resting 
upon  posts  ^,  b'^  through  which  and  the  blades  the  electric 
current  passes. 

Between  the  blades  is  a  powerful  bent  spring  r,  provided 
with  a  cross  piece  p  q,  which  lies  beneath  the  blades  and 
lifts  them  when  the  spring  is  released  from  the  latch  g.  The 
button  Sy  having  been  pressed,  contact  is  made;  it  is  broken 
by  pinching  the  latch. 

Determination  of  Time  Value  of  Record. — To  determine 
the  time  corresponding  to  a  given  reading,  let  /  be  the 
length  of  the  equivalent  simple  pendulum ;  v  the  velocity  of 
the  center  of  oscillation  or  point  b;  y  the  vertical  distance 
passed  over  by  this  point;  x  the  variable  angle  which  the 
axis  of  the  pendulum  makes  with  the  vertical;  and  t'  the 
time  necessary  for  the  point  b  to  pass  over  an  entire  circum- 
ference, the  radius  of  which  is  /,  with  a  uniform  velocity  v. 
We  then  have : 


V=: 


y/2gy. 


VI.— VELOCIMETERS. 


Substituting  for  y  its  value  in  terms  of  x,  the  above  ex- 
i:)ression  becomes  : 

^=V2^^"7cos^ 
from  which  it  is  evident  that  the  velocity  of  the  pendulum 
increases  from  its  highest  to  its  lowest  point. 

The  time  /'  is  equal  to  the  circumference  of  the  circle, 
the  radius  of  which  is  /,  divided  by  the  velocity  v;  if  this 
value  of  f  be  again  divided  by  360,  we  shall  have  very 
nearly  the  time  of  passing  over  any  degree  at  the  height  y^ 
or — 

2  7tl 


t= 


360^2^/ cos  ^. 


Calling  /"  the  time  of  a  single  vibration  of  the  pendulum 
of  the  machine,  we  have  by  known  laws — 

Substituting  this  value  in  the  equation  above,  and  represent- 
ing— 

jg^|by«,  wehave 


V  COS  X. 

To  determine  /",  the  pendulums  are  removed  from  the 
machine,  and  the  cylindrical  journals  about  which  they  re- 
volve are  replaced  by  others,  the  bearing  surfaces  of  which 
are  knife  edges.  Each  pendulum  is  started  vibrating  through 
a  very  small  arc.  By  means  of  a  stop-watch  the  time  of 
1,000  vibrations  may  be  found.  By  repeating  the  operation 
several  times  and  taking  the  mean,  the  time  of  a  single 
vibration  may  be  determined  very  exactly.  This  time  for 
pendulums  of  recent  construction  is  0.378  of  a  second. 


VI. — VfiLOClMETERS. 


If  now  X  be  made  successively  equal  to  1°,  2°,  3°,  &c., 
and  the  corresponding  values  of  /  be  found,  we  shall  have 
the  time  of  passage  of  the  pendulum  over  each  degree. 

By  adding  the  time  of  passage  over  the  first  degree  to 
that  over  the  second,  we  shall  have  the  time  of  passage 
over  an  arc  of  2°.  In  the  same  manner,  by  adding  this 
latter  time  to  that  over  the  third  degree,  we  shall  have  the 
time  of  passage  over  an  arc  of  3°,  and  so  on. 

The  following  table  has  been  determined  in  this  manner: 
Table. 


De- 

grefeB. 

Time  in  seconds 

of  passage  over 

each  degree. 

Sum  of  times  in 
seconds. 

De- 
grees. 

Time  in  seconds 

of  passage  over 

each  degree. 

Sum  of  times  in 
seconds. 

1 

.00148504 

.00148504 

19 

.00152749 

.02849909 

2 

.00148538 

.00297042 

20 

.00153174 

.03003083 

3 

.00148594 

.00445636 

21 

.00153684 

.0315676T 

4 

.00148673 

.00594309 

22 

.00154213 

.03310980 

5 

.00148775 

.00743084 

23 

.00154772 

.03465752 

6 

.00118001 

.00891985 

24 

.00155361 

.03621113 

7 

.00149019 

.01041034 

25 

.00155980 

.03777098 

8 

.00149221 

.01190255 

26 

.00156630 

.03933723 

9 

.00149415 

.01339670 

27 

.00157313 

.04091036 

10 

.00149033 

.01489303 

28 

.00158029 

.04249065 

11 

.00149876 

.01639179 

29 

.00158780 

.04407845 

12 

.00150142 

.01789321 

30 

.00159565 

.01567410 

13 

.00150433 

.01939754 

31 

.00160388 

.04727798 

14 

.00150749 

.02090503 

32 

.00161248 

.04889046 

15 

.00151089 

.02241592 

33 

.00162147 

.05051193 

16 

.00151455 

.02393047 

34 

.00:63087 

.05214280 

17 

.00151847 

.02544894 

35 

.00164070 

.05378350 

18 

.00152266 

.02097160 

36 

.00165092 

.05543442 

To  Compute  a  Scale  of  Velocities. — It  should  be  rem.em- 
bered  that  the  times  above  determined  correspond  to  but 
half  the  difference  of  the  arcs  described  by  the  two  pen- 
dulums; therefore,  they  should  be  doubled  in  order  to  get 
the  time  r. 

2.  THE  LE  BOULENGE  CHRONOGRAPH. 

See  Figures  4,  5,  8,  9. 
Description. — This  velocimeter,  invented  by  Captain  Le 
Boulenge  of  the  Belgian  artillery,  is  the  one  used  generally 
throughout    the    world   for   the   determination    of    initial 


Vt. — vfiLO^iMETERg. 


velocities.  In  it  the  masses  a  and  b  are  rods  falling 
freely  from  electro-magnets  E,  E' .  These  are  supported 
on  a  stand  s,  so  placed  that  while  a  may  fall  through  the 
foot  of  the  stand,  the  fall  of  b  is  arrested  by  a  trigger  /, 
the  shock  upon  which  releases  a  knife-shaped  marker  m. 
The  edge  of  this  marker  lies  close  to  the  path  of  a,  so  that 
a  very  slight  movement  of  it  to  the  right,  under  the  impulse 
of  a  powerful  spring  which  is  liberated  by  the  fall  of  b^ 
produces  a  mark  upon  that  elementary  circle  of  a  which 
was  opposite  to  7n  at  the  moment  of  impact. 

Disjunctor. — Although  the  operation  of  the  disjunctor  is 
the  same  as  with  the  Benton  velocimeter,  its  object  in  the 
LeBoulenge  instrument  is  quite  different. 

It  serves,  by  making  r=(9,  to  determine  the  value  of  4* 
since  then  4=4>  o^^  the  time  that  a  was  falling  before  it 
was  struck  measures  the  time  required  for  b  to  strike  it. 

This  instrument  does  not  serve  to  determine  the  signal 
time,  but  it  may  be  shown  that  if  the  difference  in  signal 
times  remains  constant  the  time  recorded  between  the 
events  =  time  between  the  epochs,  or  0=?. 

Operation. — This  mark  may  be  made  in  three  ways,  as 
follows: 

1.  Release  m  while  a  is  at  rest;  the  mark  will  fall  at  O, 
which  is  the  origin  for  future  measurements. 

2.  By  means  of  the  disjunctor,  rupture  E  and  E'  simul- 
taneously; the  mark  will  be  at  some  point  Z>  at  a  height  h 
above  O,  corresponding  to  the  time  required  for  b  to  fall  to 


m  and  for  m  to  mark  the  rod  a.     This  time  is  /, 


1 1h 


or  the  time  required  for  b  to  strike  a.     The  mark  D  is 
called  the  disjunction  mark. 

3.  Use  as  Megagraph. — Rupture  E  and  immediately 
afterward  E'\  the  mark  will  occur,  as  at  R^  at  a  height  /%' 
above   O.     This    is  the   usual    case    in    practice.      Then 


VI. — VELOCIMETERS. 


•v 


2  h' 

=  the  time  during  which  a  was  falling  before 

i 

it  was  struck,  and  t^—t^=Q^  as  with  the  Benton  velocimeter. 
The  mark  R  is  called  the  record  mark. 

As  a  matter  of  convenience  only,  the  construction  of  the 
instrument  permits  4  to  be  made  constant  =0^  15,  so  that 
a  rule  may  be  so  graduated,  that,  for  a  given  interval  be- 
tween targets,  the  velocity  corresponding  to  a  height  OR 

s  s 

may  be  obtained  by  simple  inspection,  for  v  =—= 

T     4-OM5 

The    instrument    so    arranged    is    called    a    Megagraph. 

(Greek  ^eya8,-great.) 

Use  as  Micrograph. — By  raising  E'  so  that  the  lower 
end  of  b  may  be  nearly  level  with  the  top  of  a,  D  will  be 
made  to  occur  near  that  section  of  a  which  passes  m  with 
the  greatest  velocity.  This  serves  to  verify  the  accuracy 
of  the  operation  of  the  disjunctor,  of  the  magnets,  and  of 
the  marking  apparatus;  since,  if  these  parts  worked  with 
perfect  uniformity,  successive  disjunction  marks  would  be 
found  at  the  same  height  above  O.  The  velocity  of  a  at 
the  moment  of  marking  magnifies  the  visible  consequences 
of  deficient  uniformity  and  assists  in  correcting  the  causes 
to  which  it  is  due. 

With  this  arrangement,  if  b  is  detached  before  a^  the 
mark  will  be  found  as  at  R  and  Q=t^—t^. 

The  advantages  of  this  arrangement  for  the  measure- 
ment of  very  small  intervals  of  time  give  it  the  name  of 
micrograph.     (Greek  fxiupoB^-smali.) 

Determination  of  time  limit. — The  following  reasoning 
determines  the  circumstances  under  which  the  instrument 
should  be  used  as  a  megagraph,  or  as  a  micrograph. 

Considering  for  the  moment  0r=r  and  remembering  that 
we  are  measuring  the  interval  t=-  we  see  that,  with  the  in- 

V 


VI. — VELOCIMETERS. 


strument  arranged  as  a  megagraph,  r  may  be  greatly  dimin- 
ished by  increasing  v  and  reducing  s.  The  mark  R  will  then 
be  made  near  D  where  a  has  but  little  velocity,  and  therefore 
imperceptible  differences  in  h  may  correspond  to  considerable 
differences  in  r  and  hence  in  v.  Since  the  instrument  was 
invented,  initial  velocities  have  increased  from  1,200  f.  s.  to 
over  2,000  f.  s.  while  s  may  be  restricted,  as  at  West  Point, 
so  as  to  be  reduced  from  50  metres  (164  feet,  for  which  interval 
the  instrument  was  made)  to  but  50  feet  and  even  less. 

On  the  other  hand,  when  using  the  instrument  as  a 
micrograph,  if  r  increase  unduly,  the  mark  will  occur  in 
the  same  neighborhood  as  before,  and  the  same  conse- 
quences will  ensue. 

It  becomes  therefore  necessary  to  determine  a  common 
time  limit  within  which  the  instrument  should  be  used  as  a 
micrograph  and  beyond  which  as  a  megagraph. 

For  this  time  the  mark  will,  in  both  cases,  occur  at  the 
same  height  above  O.  For  the  megagraph,  it  will  be  at 
the  height  corresponding  to  4=r  +  0^''*'-.15. 

For  the  micrograph,  since  the  length  of  ^=about  0.5 
metre,  the  maximum    value  of   /b=:0^®*^-.32;  therefore,  4= 

Qsec.32_2'. 

Equating  these  two  values  of  4,  we  have  r=0.^®^085  as 
the  value  of  the  time  limit. 

Details  of  the  Instrument. 

Chronometer. — Referring  to  the  definitions,  p.  1,  the 
rod  a  is  seen  to  be  a  register^  the  time  of  fall  of  which  to 
any  distance  h  below  the  edge  of  the  knife  making  the 
mark  (9,  is  known. 

This  rod  in  this  instrument  is  called  the  chronometer.  It 
is  enclosed  by  a  tightly  fitting  zinc  tube  which  receives  the 
marks.  By  turning  this  tube  axially,  and  finally  by  revers- 
ing it,  many  records  may  be  made  before  it  need  be  changed, 


10  VI. — VELOCIMETERS. 


Registrar. — The  rod  b  is  called  the  registrar.  It  is  much 
lighter  than  a. 

Adjustment. — To  diminish  differences  in  the  time  of  de- 
magnetization, the  power  of  the  magnets,  E,  E\  is  reduced 
to  a  safe  minimum,  which,  by  the  movable  screw-cores  con- 
tained in  the  magnets,  is  determined  as  follows: — 

A  definite  surplus  of  power*  is  assured  by  attaching  to 
each  armature  a  make-weight  in  the  form  of  a  tube  of  -^ 
the  weight  of  the  armature.  The  weighted  armature  having 
been  suspended  from  the  magnet,  the  core  of  the  latter  is 
slowly  unscrewed  until  the  armature  falls.  The  make- 
weight is  removed  before  the  armature  is  again  applied. 

Disjunction  Circle. — When  it  is  desired  to  read  velocities 
directly  from  the  rule,  the  value  of  t^  is  made  constant  by 
varying  the  height  of  fall  of  b  so  that  the  mark  shall  fall 
upon  a  disjunction  circle  previously  traced  upon  the  zinc 

recorder  at  a  height  above  O  =  ~ — ^ —  • 

Levelling. — The  instrument  is  levelled  by  using  the  sus- 
pended chronometer  as  a  plumb, 
between  the  epochs. 

Bregers  Improvemen'.s. — In  order  to  diminish  variations 
in  o'a— o'b  resulting  from  variations  in  the  method  of  rupture, 
depending  upon  whether  the  circuit  is  broken  by  the  dis- 
junctor  or  by  impact  of  the  projectile  on  the  target  wires,  the 
improvements  of  Captain  Breger  of  the  French  service 
tend: — 

1.  To  diminish  differences  in  the  time  and  velocity  of 
rupture  of  the  two  circuits  by  the  disjunctor,  which  differ- 
ences are  due  to  the  unequal  operating  of  the  parts  of  the 
disjunctor. 

Such  differences  are  found  to  make  material  differences 
in  the  times  required  to  demagnetize  E,  E',  in  consequence 
of  variations  in  the  intensity  of  the  induced  currents  follow- 
ing variations  in  the  method  of  rupture. 


VI. — VELOCIMETERS.  11 

2.  Differences  in  the  rate  of  demagnetization  have  been 
avoided  by  making  as  nearly  equal  as  possible  the  masses 
a  and  b,  and  therefore  the  magnetic  states  of  E  and  E'. 

These  and  other  minor  mechanical  improvements  have 
diminished  the  mean  error  to  ^  of  that  form.erly  found. 

CLASS  II. 

Register. — The  register  in  these  instruments  generally 
consists  of  a  revolving  polished  metallic  cylinder,  the  angu- 
lar velocity  of  which  is  known.  The  surface  of  the  cylinder 
is  preferably  smoked,  so  as  to  make  visible  the  marks  which 
it  receives. 

Marks. — The  marks  are  made  in  two  general  ways; — 

1st.  By  the  trace  of  a  quill  point  held  lightly  against 
the  cylinder. 

By  giving  the  quill  point  relative  longitudinal  motion 
during  the  rotation  of  the  cylinder,  the  trace  may  be 
greatly  developed  helically. 

This  trace  being  developed  during  the  motion  of  the 
projectile,  the  latter's  arrival  at  an  epochal  point  may  be 
signalized  by  a  sudden  motion  of  the  quill  point  along  a 
rectilinear  element  of  the  cylinder,  causing  a  jog  or  offset 
in  the  trace.    See  Fig.  6.     The  offset  is  here  the  mark. 

This  motion  may  be  caused  by  the  action  of  a  spring 
previously  in  equilibrium  with  the  attraction  of  an  electro- 
magnet. This  magnet  is  included  in  a  circuit  that  is  broken 
by  the  arrival  of  the  projectile  at  the  epochal  point. 

If  the  circuit  can  be  re-established  before  the  next 
epochal  point  is  reached  by  the  projectile,  the  quill  point 
will  return  to  the  prolongation  of  the  trace,  and  one  quill 
point  will  suffice.  Otherwise,  as  in  Fig.  6,  as  many  quill 
points  and  circuits  are  needed  as  there  are  epochal  points. 

3nd.  The  mark  may  result  from  the  passage  of  an 
induced  electric  spark  caused  by  the  rupture  of  a  primary 
circuit  at  each  epochal  point. 


13  VI. — VELOCIMETERS. 


Signal  Times. — In  order  to  avoid  variations  in  the  time 
of  signaling,  it  is  advisable,  in  both  cases  above  cited,  to 
include  all  the  epochal  points  in  the  same  circuit  and  to 
provide  each  of  them  with  the  means  of  renewing  the 
broken  circuit  automatically  before  the  projectile  can  arrive 
at  the  next  point.     See  Targets,  Class  II,  below. 

When  the  times  to  be  measured  are  exceedingly  minute, 
this  may  not  be  feasible.  Equality  in  signal  times  is  then 
sought  by  increasing  the  delicacy  of  the  apparatus  and 
is  verified  by  the  simultaneous  rupture  of  as  many  circuits 
as  there  are  markers  to  be  operated. 

Tuning  Fork. — Uniformity  in  the  rotation  of  the  cylinder 
is  either  assumed  from  the  accuracy  of  the  apparatus  or 
may  be  neglected  by  attaching  a  tracing  quill  to  one  of  the 
tines  of  a  tuning  fork,  the  time  of  vibration  of  which  is 
known. 

The  trace  then  takes  the  form  of  a  harmonic  curve,  the 
alternate  intersections  of  which  with  a  median  trace,  formed 
when  the  fork  is  at  rest,  mark  the  ends  of  each  double 
vibration  of  the  fork. 

The  duration  of  the  double  vibration  is  the  unit  of 
measure  of  time;  if  the  velocity  of  the  surface  upon  which 
the  trace  is  formed  be  constant  during  any  double  vibration, 
fractional  parts  of  the  intercepted  median  line  will  measure 
corresponding  portions  of  the  unit  of  time. 

The  double  vibration,  instead  of  the  single  vibration,  is 
selected  as  the  unit  in  order  to  neutralize  errors  of  meas- 
urement. The  median  line  gives  the  most  definite  inter- 
sections with  the  harmonic  curve. 

Interrupter. — When  the  total  time  of  the  observation  re- 
quires it,  the  vibrations  of  the  fork  F,  Fig.  7,  may  be  sustained 
by  the  use  of  adjacent  electro-magnets,  w,  w,  the  attrac- 
tion of  which  separates  the  tines,  /,  t,  until  the  rupture  of  the 
circuit  through  the  spring  R^  releases  them.     The  spring  is 


VT. VELOCIMETERS. 


13 


used  instead  of  a  rigid  contact  so  as  to  prolong  the  influ- 
ence of  the  magnets.  The  reaction  of  the  fork  due  to  its 
elasticity  renews  the  circuit  and  makes  the  process  con- 
tinuous. 

This  device,  as  applied  to  the  Schultz  Chronoscope,  is 
known  in  this  country  as  the  Russell  interrupter.  It  is  due 
to  Captain  Russell  of  the  Ordnance  Department. 

When  the  total  time  of  vibration  is  very  short,  no  inter- 
rupter is  required.  In  this  case  the  fork  may  be  set  vibrat- 
ing by  the  sudden  withdrawal  of  a  wedge  inserted  between 
its  tines;  it  is  then  abandoned. 

CLASS  III. 

In  instruments  of  this  class  relative  motion  is  given  to 
the  register  directly  by  the  motion,  either  of  the  piece  or 
of  the  projectile. 

The  velocity  of  the  register  at  any  portion  of  its  path  is 
determined  by  tracing  upon  it  a  harmonic  curve  with  the 
tuning  fork,  or  by  giving  it  a  known  velocity  at  right  angles 
to  that  of  the  moving  part.  In  either  case,  a  compound 
curve  is  traced  from  which  the  required  relations  between 
space  and  time  may  be  deduced. 

Examples: — 

If  to  a  gun  about  to  recoil  be  fastened  a  bar  upon  the 
smoked  surface  of  which  the  harmonic  curve  is  traced  dur- 
ing the  recoil,  or  if  some  point  of  the  gun  be  kept  in  con- 
tact with  a  cylinder  rotating  at  a  known  velocity  about  an 
axis  parallel  to  the  direction  of  the  recoil,  we  may  in 
both  cases  determine  by  interpolation  the  velocities  desired: 

For  example: — 


Travel 

Time. 

A/ 

A  X 

ft. 
0.00 
0.02 

0.04 

sec. 
0.0000000 
0.0018182 
0.0023772 

sec. 

0.0018182 
0.0005590 

f.  S. 

11.0 
35.8 

14  VI. — VELOCIMETERS. 

Knowing  thus  the  mean  velocities  between  many  pairs 
of  epochal  pjints,  it  is  possible  by  interpolation  to  deter- 
mine the  accelerations  at  each  of  the  epochal  points  and, 
knowing  the  mass  of  the  moving  object,  to  determine  the 
intensity  of  the  pressure  accelerating  it. 

TARGETS. 

CLASS    I. 

The  epochal  points  are  generally  wire  screens  stretched 
across  the  trajectory,  as  shown  in  Fig.  9. 

Cannon. — In  order  to  prevent  injury  to  the  first  screen 
and  to  allow  for  the  acceleration  of  the  projectile  for  a 
short  distance  after  it  has  left  the  muzzle,  due  to  the  rela- 
tively great  velocity  of  the  escaping  gas,  the  first  screen  is 
put  at  a  distance  from  the  muzzle,  which  increases  with  the 
calibre  of  the  gun. 

When  they  are  situated  in  the  bore  of  the  gun,  as  in  Cap- 
tain Noble's  experiments,  Figs.  11  and  12,  the  wire  may  be 
severed  by  the  action  of  a  wedge  raised  by  the  passage  of 
the  projectile.  This  arrangement  requires  the  walls  of  the 
gun  to  be  pierced  radially  as  many  times  as  there  are 
epochal  points. 

To  avoid  this  piercing,  the  L^tard  apparatus.  Fig.  10,  is 
devised.  It  is  principally  of  wood,  cemented  by  resin  to 
the  surface  of  the  bore.  The  head  ot  the  metaUic  bolt,  a, 
and  the  metallic  washer,  b,  are  held  in  contact  by  the  cross 
pin,  c.  The  impact  of  the  projectile  on  the  point  of  a  breaks 
the  circuit  and  sweeps  the  fragments  out  to  the  front. 

Small  Arms. — For  small  arms,  in  order  to  save  the  time  re- 
quired in  repairing  at  each  fire  the  distant  target,  it  consists 
of  an  iron  plate  having  attached  to  its  back  a  flat  elastic 
blade,  through  which  the  circuit  passes  as  in  the  disjunctor, 
Fig.  3.  The  shock  of  impact  breaks  the  circuit  which  is 
immediately  re-established  by  the  elasticity  of  the  blade. 


VI. — VELOCIMETERS.  15 


CLASS   II. 

Instruments  of  this  class  that  use  but  one  circuit  for  all 
the  targets  have  an  arrangement,  shown  in  Fig.  13. 

The  weights,  IV,  depress  the  free  ends  of  the  spring  wire 
staples,  df  d,  f,  so  that  the  current  may  pass  from  the  brass 
plate,  ay  to  the  brass  plate,  <r,  through  the  staple,  bj  and  from 
^  to  ^  through  d,  and  so  on. 

When  one  of  the  threads  /  is  broken  by  the  projectile, 
the  free  end  of  one  of  the  tines  of  d  flies  upward,  break- 
ing the  circuit  for  an  instant,  but  renewing  it  as  soon  as  the 
upper  side  of  the  oblong  hole  in  c  is  reached. 

The  West  Point  target,  figure  15,  resembles  that  above 
described,  but  is  applied  to  instruments  of  Class  I. 

A  discontinuous  copper  strip,  c,  c,  c,  conveys  the  current 
when  the  flanged  copper  tubes  /,  t  (cartridge  cases),  are  drawn 
into  place  by  the  weights  w,  w. 

When  a  weight  is  cut  the  spring,  s,  lifts  its  tube  and  the 
circuit  is  broken. 

Compared  with  fig.  9,  the  advantages  are  — 

1.  The  circuit  is  broken  in  the  same  manner,  both  by  the 
disjunctor  and  by  the  projectile.     See  page  10. 

2.  The  tension  of  the  threads  and  the  resistance  of  the  cir- 
cuit are  more  constant  than  when  a  spHced,  continuous  target 
wire  is  used. 

3.  The  targets  are  more  readily  mended,  and  the  "  short 
circuiting  "  of  leading  wires  by  fragments  of  the  target  wires 
is  avoided. 

ELECTRIC    BATTERIES. 

These  should  be  as  constant  as  possible.  Where  storage 
room  permits  the  employment  of  a  large  number  of  elements, 
the  batteries  of  the  gravity  type  are  preferred,  except  for  pro- 
ducing the  sparks  referred  to  on  page  11. 


VII. — PRESSURE   GAUGES. 


CHAPTER  VII. 

PRESSURE   GAUGES. 
Object. 

From  the  circumstances  of  the  case  the  transfer  of  energy 
from  the  gunpowder  to  the  projectile  is  accompanied  by  a 
considerable  elastic  pressure  upon  the  walls  of  the  gun, 
the  effects  of  which,  to  be  guarded  against,  require  the 
intensity  of  the  pressure  to  be  known. 
History. 

Owing  to  the  want  of  suitable  apparatus,  pressures  were 
formerly  inferred  only  from  the  injury  resulting  to  the  gun, 
and  it  was  not  until  the  time  of  Rodman  that  this  important 
requisite  was  supplied.  Since  then  great  improvements  have 
been  made,  some  of  which  will  be  described. 
Nature  of  Pressure. 

The  pressure  varies  at  each  instant  during  the  passage  of 
the  projectile  through  the  bore,  and  is  generally  taken  to  be 
constant  throughout  the  volume  in  rear  of  the  projectile  at 
any  point  of  its  path.  If  we  adopt  Noble's  hypothesis, 
hereafter  to  be  explained,  this  is  equivalent  to  saying  that 
the  gases  in  rear  of  the  projectile  at  any  instant  are  of  uni- 
form density. 

But  the  expansion  to  the  front  and  rear,  in  consequence 
of  the  motion  of  the  projectile  and  of  the  piece,  diminishes 
the  density  of  the  successive  layers,  estimated  in  both  direc- 
tions from  that  layer  containing  the  center  of  gravity  of  the 
system.  This  layer,  called  the  immovable  layer,  is  practi- 
cally taken  at  the  bottom  of  the  bore,  where  experiment 
shows  that  the  maximum  pressures  occur.    See  page  17. 


VII. — PRESSURE   GAUGES. 


General  Methods  Adopted. 

Two  general  methods  for  measuring  the  intensity  of  the 
pressure  are  employed,  viz.: 

1.  Statical. 

The  statical,  in  which  the  elastic  pressure  is  placed  in 
equilibrio  with  a  known  resistance.  The  objections  to  this 
method  relate  to  the  magnitude  of  the  forces  to  be  measured 
and  to  the  rapidity  with  which  they  vary.  It  is  principally 
valuable  for  determining  the  intensity  of  the  maximum 
pressure  at  the  point  at  which  the  measurement  is  made. 

2.  Kinetic. 

In  which  the  intensity  of  the  pressure  at  any  instant  is 
deduced  from  the  acceleration  given  to  a  known  mass. 

The  objections  to  this  method  relate  to  the   minuteness  of 

the  times  to  be  measured  and  to  the  consequences  of  small 

.        .                   .                A''^ 
errors  m  measurmg  the  spaces,  smce  a= 

By  the  use  of  comparatively  simple  apparatus  it  permits 
the  law  of  the  variation  in  pressure  to  be  approximately 
determined. 

I.-THE  STATIC   METHOD. 
Rumford's  Plan. 

In  1792,  Count  Rumford,  who  made  the  first  recorded 
experiments  on  powder  pressures,  sought  to  measure  the 
total  pressure,  P=/  7t  r%  of  a  charge  of  gunpowder  fired  in 
the  closed  bore  of  the  eprouvefte,  Fig.  1,  by  determining 
the  greatest  weight,  W,  that  would  be  lifted  by  the  gas  suffi- 
ciently to  allow  the  escape  of  gas  to  cause  an  audible  report. 
Conversely,  the  weight  and  the  volume  being  constant,  he  varied 

W 
the  charge.     In  either  case  he  assumed  P—  W  oi  fiz=. r 

But  if  we  represent  by  /,  the  time  during  which  the  gases 
were  lifting  the  tenon  of  the  stopper  through  the  height  h^ 


VII. — PRESSURE    GAUGES. 


the     general     expression     Mgl  =  M  =  P-  JV,    (whence 


/i  = 


F^W 


df 


t  \  '^^ 

yf^      ^  J  shows  that,  /  being  very  small,  P  must  have 

greatly  exceeded  W  in  order  that  h  should  have   had  an 
appreciable  value. 
Process  of  Deformation. 

This,  which  is  the  present  method,  consists  — 

1st.  In  determining  with  a  press  the  tarage^  or  law  con- 
necting known  pressures  with  the  observed  permanent  de- 
formations of  similar  metallic  specimens. 

2nd.   Exposing  a  similar  specimen  to  the  action  of  powder 
gases   acting   over  a  known   area;  observing   the   resulting 
deformation,  and  inferring  from  the   tarage  the  intensity  of 
the  total  pressure  producing  the  deformation  observed. 
Methods  of  Deformation. 

The  specimen  may  be  deformed  in  several  ways — 

1.  By  making  a  cut,  the  length  of  which  increases  more 
rapidly  than  its  width.     Fig.  2. 

This  is  General  Rodman's  plan. 

2.  By  compressing  a  cylinder  between  flat  surfaces. 
This  is  Captain  Noble's  crusher  gauge,  now  generally 

employed. 

Both  methods  are  adapted  for  service  either  within  or 
without  the  bore. 

Apparatus, 
Specimens. 

On  account  of  its  homogeneity,  copper  is  generally  used  for 
the  specimen,  although  lead,  and  even  silver,  are  employed. 
Pistwi. 

The  pressures  are  exerted  through  a  freely  moving  piston. 
When  firing,  a  gas  check  of  some  kind  prevents  the  gas  from 
leaking  past  the  piston. 
Gas  Checks. — 1.  Cup. 

The  action  of  this  gas  check,  which  illustrates  a  principle 
of  frequent  application  in  ordnance,  depends  upon  the 
excess  of  the  pressure  within  the  cup  over  that  without  it; 


VII. — PRESSURE   GAUGES. 


since  any  gas  that  may  leak  past  the  edge  before  it  is 
fully  dilated  will  expand  so  readily  as  to  have  its  density 
greatly  reduced  in  comparison  with  that  of  the  gas  within 
the  cup. 

2.  Air  Packing, 

Another  form  of  gas  check  depends  upon  a  number  of 
circumferential  grooves,  surrounding  the  stem  of  a  closely 
fitting  piston,  Fig.  4.  These  diminish  successively  the 
tension  of  any  intruding  gas  and  delay  its  progress,  until, 
by  the  departure  of  the  projectile  from  the  gun,  the  pres- 
sure ceases.  This  principle  also  is  applied  in  ordnance 
construction. 
External  Housing. 

For  external  use  the  gauge  is  contained  in  a  housings 
screwed  into  the  walls  of  the  gun  and  communicating  by  a 
radial  hole  with  the  bore.  This  method  is  rarely  employed 
at  present.  ^ 

Internal  Housing. 

For  internal  service  a  housing,  Fig.  3,  contains  all  the 
parts.  The  drawing  represents  a  Noble  internal  crusher 
gauge,  full  size. 

A  is  the  specimen;  B,  the  cavity;  C  the  body  of  the 
housing,  closed  by  the  screw  y  and  the  soft  metallic  gasket  K. 

I  is  the  piston,  the  cross  section  of  which  is  y^^  of  a 
square  inch  in  area.  It  is  enlarged  at  E  to  accommodate 
itself  to  the  dilatation  of  A. 

Z>  is  a  cup-shaped  copper  gas-check  acting  like  a  metal- 
lic cartridge  case,  and  F  is  a  spring  to  keep  the  specimen 
in  an  axial  position. 

Use  of  Internal  Gauge. 

To  use  the  gauge,  it  is  tied  to  the  bottom  of  the  cartridge 
so  that  no  powder  can  pass  between  it  and  the  bottom  of 
the  bore. 


VII. — PRESSURE   GAUGES. 


It  is  sometimes  recessed  into  the  face  of  the  block  of 
breech  loading  guns,  so  that  full  charges  may  be  fired.     It 
has  also  been  similarly  recessed  into  the  base  of  the  pro- 
jectile. 
Advantages  of  Crusher  over  Rodman  Gauge. 

The  advantages  of  the  Crusher  over  the  Rodman  gauge 
are: 

1.  Size. 

The  small  diameter  of  the  specimen,  which  enables  the 
size  of  the  housing  to  be  greatly  reduced. 

When  used  internally,  the  circumstances  are  therefore 
more  nearly  normal,  and,  when  used  externally  as  in  Fig.  13,  it 
maybe  inserted  close  to  the  walls  of  the  bore  instead  of  ex- 
ternally to  the  gun  as  with  Rodman's  first  gauge.  Fig.  2. 

In  the  latter  case  it  was  found  that  the  gas  developed  con- 
siderable kinetic  energy  in  its  passage  through  the  walls 
of  the  gun  and  struck  the  pi.ston  a  blow  which  vitiated  the 
results  of  the  experiment.  This  action  accounts  for  many 
anomalies  in  the  early  experiments. 

When  properly  used,  the  fact  that  the  gases  act  by  a 
pressure  and  not  by  a  blow  is  shown  by  the  sensible  persist- 
ence of  form  of  a  specimen  exposed  to  several  similar  dis- 
charges, and  by  the  experimental  verification  of  calculations 
based  upon  this  statical  hypothesis. 

2.  Surface. 

The  flat  face  of  the  piston  is  less  liable  to  injury  and 
admits  of  duplication  more  easily  than  does  the  Rodman 
knife. 

3.  Tarage. 

It  also  admits  of  giving  to  the  specimen  a  preliminary 
compression  before  it  is  exposed  to  the  action  of  the  gas. 

This,  if  nearly  equal  to  that  expected  within  the  gun, 
diminishes  the  velocity  which  the  piston  can  acquire  (see 
^ost) ;  it  also  serves  to  verify  the  tarage. 


VII. — PRESSURE    GAUGES. 


EFFECT    OF    VARYING    THE    MASS    OF    THE    PISTON. 

Discussion.  % 

Let  /*  be  the  variable  gaseous  pressure  on  the  piston ;  R  the 
variable  resistance  to  deformation  of  the  specimen;  m  the 
mass  of  the  piston,  and  v  its  variable  velocity  over  the 
path  X. 

Let  d  represent  the  permanent  compression. 

Suppose  the  piston  to  be  in  contact  with  the  specimen 
and  to  be  indeformable. 

We  have: 

'  ^/lPdx-/lRdx.  (1) 


2 

When  X  is  a  maximum,  v—o\  x^^d,  and  the  equation  (1) 
becomes 

/\pdx=f\Rdx.  (2) 

Let  the  curves  AFE  and  BFC  in  Fig.  5  represent  by 
their  ordinates,  respectively,  the  resistances  and  pressures 
due  to  successive  values  of  x,  and  let  x  represent  only 
permanent  deformation,  /.  <?.,  that  occurring  beyond  the 
elastic  limit  of  the  specimen. 

From  the  nature  of  powder  pressures  as  hereafter  ex- 
plained, Chap.  XI,  the  pressure  curve  will  be  of  the  general 
form  OABC\  and,  if  OD—d,  we  have  area 

OABCDrz^f'^^Pdx, 

From  the  nature  of  the  resistances  to  deformation,  the 
curve  AFE  will  present  no  maximum  phase,  and  the  curve 
will  be  of  the  general  form  AFE,  such  that  the  area 

OAEn=^  f^'Rdx. 


■/> 


Equations  1  and  2  show  that  the  resistance  curve,  at  first 
beneath  the  pressure  curve,  rises  above  it  when  x  has  some 
value  =  OH, 


Vn. — PRESSURE   GAUGES. 


The  statical  value  of  the  ordinate  E,D^  corresponding  to  the 
maximum  compression  OD,  is  determined  from  the  tarage. 

The  figure  shows  that,  while  ED  may  be  greater  or  less 
than  IB^  which  represents  the  maximum  gaseous  pressure, 
the  difference  between  these  two  ordinates  will  depend 
upon  the  angle  at  which  the  curves  intersect.  If  this  angle 
be  such  that  the  difference,  P — R,  of  any  two  ordinates 
corresponding  to  a  common  abscissa  be  relatively  small,  the 
resistance  corresponding  to  the  maximum  compression  may 
safely  be  taken  as  the  maximum  gaseous  pressure. 

But  P-R=      ^         ^  ,=  ma  (3) 

doc 

So  that  the  difference  between  ED  and  IB  can  be 
neglected  only  when  the  mass  of  the  piston  is  small  and  the 
initial  resistance  to  deformation  is  great  and  increases  rapidly. 

The  last  two  conditions  are  satisfied  by  a  preliminary 
deformation  of  the  specimen  to  nearly  the  total  extent  that 
is  expected.     Such  conditions  are  represented  by  figure  6. 

The  indications  of  the  gauge  will  be  more  correct  when 
the  pressure  curve  approaches  parallelism  with  the  axis  of 
X.  It  will  be  seen  that  this  occurs  rather  with  slow-burn- 
ing powders,  which  give  a  gradual  change  of  pressure,  than 
with  those  which  act  more  violently. 

Tarage. 

The  preceding  discussion  shows  that  the  pressures  used 
in  determining  the  tarage  must  be  applied  so  slowly  that  the 
velocity  of  the  piston  and  of  the  contiguous  parts  of  the 
machine  may  be  neglected.  Under  such  circumstances, 
when  the  specimen  is  of  pure  copper,  8  mm.  in  diameter 
and  13  mm.  long,  the  resistance  in  kilogrammes,  T,  corres- 
ponding to  a  permanent  compression  in  millimetres,  E^  is 
given  by  the  following  equation. 


VII. — PRESSURE   GAUGES. 


^=551 +531  E, 
The  tarage  would  accordingly  be  represented  by  a  dia- 
gram, such  as  Fig.  7,  the  initial  ordinate  being  at  the  elastic 
limit,  and  the  co-efficient  531=tan  ^,  or  the  reciprocal  of 
the  rate  of  permanent  compression. 

V  SARRAU'S   DEDUCTIONS. 

An   elaborate    deduction   by  M.    Sarrau,   shows  by   an 
analysis  confirmed  by  experiment  that,^- 
Slow  Pressure. 

I.  When  the  pressure  increases  slowly,  as  when  the 
crusher  is  used  in  the  chamber  of  a  gun  firing  ordinary 
gunpowder,  the  maximum  pressure  is  sensibly  equal  to  that 
indicated  by  the  tarage. 

ftuick  Pressure. 

II.  When  the  pressure  is  instantaneously,  or  very  sud- 
denly applied,  as  with  some  of  the  high  explosives;  or 
when,  with  ordinary  gunpowder,  the  crusher  is  placed  in 
front  of  the  position  occupied  by  the  projectile  when  at 
rest  so  that  the  pressure  shall  be  very  suddenly  applied 
when  the  base  of  the  projectile  has  passed  the  mouth  of  the 
hole;  then  the  maximum  pressure  is  sensibly  equal  to  that 
corresponding  to  half  the  tarage. 

The  correction  increases  with  the  mass  of  the  piston 
employed. 

THE   MANOMETRIC    BALANCE. 

Object. 

This   avoids  the  perturbations  due  to  the  mass  of  the 
piston,  and  permits  certain  relations  between  pressures  and 
time  to  be  determined. 
Simple  Form. 

B,  figure  8,  is  a  differential  piston,  the  small  end  of  which 
is  in  contact  with  the  bore,  and  the  large  base  of  which  enters 
slightly  the  air-tight  cavity  C,  connected  with  a  manometer 


VII. — PRESSURE   GAUGES. 


tube,  M,  in  which  mercury  is  kept  at  any  given  height  by 
means  of  air  pumped  into  C. 

A  slide,  a,  is  held  by  friction  beneath  B  against  the  ten- 
sion of  a  spring,  r. 

The  pressure  may  be  determined  within  limits  by  finding 
at  two  successive  similar  fires,  the  heights  of  the  mercury 
permitting  and  preventing  the  motion  of  a. 

Compound  Form. 

Also  by  providing,  say,  ten  similar  pistons  of  varying 
area,  moving  outwardly  from  Cj  each  of  them  provided, 
besides  the  arrangement  ra,  with  some  apparatus  such  as 
described  Chap.  VI,  for  recording  the  intervals  of  time 
corresponding  to  the  motion  of  the  slide  a. 

II.  THE  KINETIC  METHOD. 

This  consists  in  determining  the  rate  of  change  of  the 
pressure  from  the  change  in  rate  of  motion  of  some  body, 
the  mass  of  which  is  known.  This  body  may  be  either 
I,  the  projectile;  II,  the  cannon;  or  III,  a  piston  or  auxiliary 
projectile,  placed  in  some  radial  channel  communicating 
with  the  bore. 

I.    THE    PROJECTILE. 

1.  Direct  Intermittent  Method, 

Mayewski's  Experiments.    Figure  16. 

General  Mayewski,  of  Russia,  in  1867,  attempted  to 
determine  the  acceleration  of  the  projectile  by  attaching  to 
its  base  a  rod  which,  passing  through  the  breech  of  the 
gun,  ruptured  by  means  of  a  projection  upon  it  certain 
electric  currents  placed  at  varying  distances  from  the 
initial  position  of  this  projection.  The  conditions  of  each 
fire  were  made  constant,  except  as  to  the  portion  of  the 
path  of  the  projectile,  the  duration  of  which  was  to  be 
measured. 


10  VII. — PRESSURE    GAUGES. 

Supposing  that  x~f[t),  he  assumed  a  development 

x=At+Bt^-{-Ct^  +  nt''  +  Qtc.,  (4) 

and  determined  by  trial  the  values  for  the  co-efficients,  A,  B^ 
etc.,  that  would  satisfy  the  instrumental  values  x  and  /. 
Then, 

dx 
dt 


=A^%Bt-{-ZCt^  +  ^nt^^-tio.  (5) 


d^x 
a=-^=2B  +  %Ct+12nt^  +  ttc,  (6) 

The  value  of  t  corresponding  to  the  manimum  pressure 

d^x 
wasfoundby  placing— 3  =0,  and  solving  with  respect  to  /; 

then,  by  substitution  in  equations  (1)  and  (3),  the  corres- 
ponding values  of  x  and  a  were  found. 

The  intensity  per  unit  of  area  of  the  corresponding  pres- 
sure, is  given  by  the  following  equation: 

d'^x 

This  pressure  is  only  that  giving  acceleration  to  the 
projectile.  The  results,  found  by  adding  to  B=p  n  r^  the 
pressure  found  to  be  required  to  force  the  projectile 
through  the  bore,  gave  reasonably  close  approximations  to 
the  results  of  the  statical  pressure  gauges,  altiiough  the 
apparatus  was  subject  to  many  instrumental  errors. 


2.  Direct  Continuous  Method, 
Sebert's  Registering  Projectile. 

This  method,  which  is  applicable  only  to  comparatively 
short  lengths  of  bore  in  guns  of  large  caliber,  requires  a 
hollow  cylindrical  projectile,  such  as  is  shown  in  Fig.    9.     It 


VII. — PRESSURE    GAUGES.  11 

is  provided  with  an  axial  spindle,  S,  of  rectangular  cross 
section  and  rotating  freely  at  each  end;  one  of  the  sides  of 
this  spindle  is  covered  with  a  film  of  soot. 

A  slide  M  moves  freely  on  the  spindle  and  bears  a 
delicate  tuning  fork  7^  arranged  as  described,  Chap.  VI. 

When  the  projectile  is  fired,  the  inertia  of  the  slide  holds 
it  relatively  at  rest  while  the  projectile  passes  by;  the 
points  of  the  tines  describe  such  a  trace  as  is  shown  in 
figure  10,  in  which  the  parallel  straight  lines  represent  the 
traces  when  the  slide  is  slipped  along  the  spindle,  the  fork 
not  vibrating. 

The  effect  of  the  friction  between  the  slide  and  the 
spindle  can  be  shown  to  be  negligible. 

Although  the  path  of  the  slide  is  limited  to  less  than  the 
length  of  the  projectile,  yet  it  is  within  this  length  of  travel 
that  is  generally  found  the  maximum  pressure,  the  rate  of 
change  in  reaching  which  is  one  of  the  most  important 
objects  of  research. 

By  placing  the  slide  at  the  bottom  of  the  spindle,  it  may 
serve  to  determine  the  retardation  of  the  projectile  in  flight; 
and,  by  confining  it  there  by  a  fragile  cross-pin  to  be  broken 
on  impact,  it  may  determine  the  varying  resistance  found  in 
penetrating  a  more  resisting  medium  than  the  air. 

3.  hidirect  Intermittent  Method. 
Successive  Shortening  of  the  Bore. 

The  mean  of  the  muzzle  velocities  of  a  large  number  of 
shots  fired  under  conditions,  which,  excepting  the  length  of  the 
bore,  were  identical,  could  be  laid  off  as  the  ordinates  of  a 
curve  of  which  the  abscissae  should  represent  the  various 
paths.  The  curve  would  have  the  form  given  by  Fig.  11. 
Calling  a  the  acceleration,  we  have, 

dv       dv      dx  dv  /i\ 

dt      dx        dt         dx 


12  VII. — PRESSURE    GAUGES. 


The  figure  shows  that  the  subnormal  a=  corresponding 

ordinate  v  x  tan  g?  =  ?;  x  -r-  •  (") 

^  ax 

Therefore,  having  plotted  the  curve  expressing 
v=f(x), 
the  acceleration  at  the  different  points  along  the  bore  may 
be  determined  by  finding  the  corresponding  values  of  the 
subnormals. 

The  experiments  enabled  positive  conclusions  to  be 
formed  : 

1st.  As  to  the  smallness  of  the  advantage  gained  by  in- 
creasing the  length  of  the  bore  more  than  20  calibers,  when 
quick  powders  were  used. 

2nd.  As  to  the  great  advantage  of  progressive  powders  in 
guns  of  suitable  length. 

II.    THE    GUN. 

Advantages. 

Determining  the  pressure  from  the  acceleration  of  the  gun 
in  its  recoil  affords  certain  advantages  owing: — 

1st,  To  the  low  velocity  of  the  gun  compared  to  that  of 
the  projectile;  this  permits  a  greater  number  of  observations 
to  be  made  over  a  given  path. 

2d.  To  the  simplicity  of  the  apparatus,  which  avoids  the 
mutilation  of  the  piece,  and  permits  it  to  be  used  with  guns 
of  varying  calibers. 

3d.  To  the  aid  given  in  the  study  of  the  pressures  pre- 
vailing at  the  bottom  of  the  bore. 

1.  Rodman's  Velocimeter , 
Construction. 

The  original  instrument  of  this  description  was  devised 
by  General  Rodman.  It  consisted  of  a  cylinder  rotating 
with  a  known  and  uniform  velocity  about  an  axis  parallel 


Vll. — PRESSURE   GAUGES.  13 

to  that  of  the  gun  and  close  to  it,  A  pointer  fastened  to 
the  gun  traced  upon  the  cylinder  during  the  recoil,  a  line 
which,  when  developed,  gave  the  successive  accelerations  of 
the  recoil.  The  gun  was  hung  as  a  pendulum  oscillating 
in  the  plane  of  fire.     See  figure  17. 

Acceleration  of  Eecoil. 

For  example,  let  mm' ^  Fig.  12,  be  the  developed  circumfer- 
ence traced  by  the  pointer  when  the  projectile  is  placed  at  the 
muzzle,  and  the  charge  uniformly  dispersed  along  the  bore ; 
and  let  bb'  be  the  corresponding  circumference  when  the  charge 
is  in  place.     Then  taking  axes  of  space  and  time,  ^S"  and  T 

a  =  7 — -ri,  as  in  Chap.  VI. 

Tlniform  Pressure. 

The  dotted  line  represents  the  parabola  which  would  be 
traced  under  the  ideal  circumstances  discussed,  Chap.  V, 
/  V  being  straight  and  parallel  to  t'  v' . 

Rate  of  Change  of  Pressure. 

It  is  evident,  from  the  inclination  of  the  initial  portions 
of  the  curve,  that  ihe  velocity  is  actually  acquired  much  more 
rapidly  than  is  desired. 

2.  Siberfs  Velocimeter, 

Construction. 

The  velocimeter  of  Colonel  Sebert  of  the  French  service 
replaces  the  rotary  cylinder  by  a  broad  steel  tape,  one  side 
of  which  is  smoked,  and  against  which  rest  the  tines  of  a 
tuning  fork  set  vibrating  by  the  act  of  recoil.  See  Chap. 
VI. 

Velocity  of  Recoil. 

The  length  of  any  double  vibration  measured  on  the 
tape,  divided  by  the  time  of  the  double  vibration  of  the 


14  Vll.— PRESSURE  GAUGES. 

fork,  gives  us  the  mean  velocity  of  recoil  over  that  portion 
of  the  path  selected;  from  which,  calling, 

qv   =z  weight  of  projectile. 

JV  =  weight  of  gun. 

«/  =  weight  of  powder. 

2j    =  velocity  of  projectile. 

V    =  velocity  of  gun. 

We  have  V=  -^  (see  Chapter  VI). 

Velocity  of  Projectile. 

Or  else,  supposing  the  center  of  mass  of  the  powder  to  be 
moved  to  the  position  occupied  by  the  center  of  mass  of  the 
gases,  which  is  equivalent  to  supposing  that  half  the  mass  of 
the  powder  is  added  to  that  of  the  projectile. 

-=  --^r  (9) 

Position  of  Projectile. 

Also,  denoting  by  X  the  length  of  recoil  at  the  end  of  a 
time  t,  and  x  the  corresponding  path  of  the  projectile. 

Pressure  on  Base  of  Projectile. 

The  method  above  described  permits  the  construction  of 
a  velocity  curve,  such  as  Fig.  11,  from  which  the  pressure 
corresponding  to  different  positions  of  the  projectile  along 
the  bore  may  be  deduced. 
Pressure  on  Base  of  Bore. 

Also,  the  difference  between  two  successive  velocities,  as 
determined  by  the  trace  of  the  tuning  fork,  divided  by  the 
common  interval  of  time,  would  give  the  mean  accelera- 
tion ;  this  multiplied  by  the  mass  of  the  gun  gives  the  mean 


Vn, — PRESSURE  GAUGES.  15 


total  pressure  on  the  bottom  of  the  bore  during  the  same 
interval  of  time. 

III.    AUXILIARY    PROJECTILES   EXPELLED    THROUGH   THE 
WALLS   OF    THE    GUN. 

1.  Bomford's  Method. 

About  1841,  Colonel  Bomford,  of  the  Ordnance  Depart- 
ment, prepared  a  cannon  by  boring  through  its  walls  a 
series  of  small  holes  at  right  angles  to  its  axis,  as  in  Fig.  13, 
and  placing  in  each  hole  a  bullet,  the  velocity  of  which  was 
instrumentally  determined.  The  pressure  at  the  various 
points,  deduced  from  the  velocities  communicated  to  the 
balls,  determined  the  form  of  the  old  Columbiads. 

This  method  was  objectionable,  as  it  treated  the  powder 
pressure  as  an  impulsive  force  and  could  not  take  into 
account  the  varying  accelerations  of  the  projectile,  as  is 
done  in  the  following  recent  inventions. 

2.  Ricqs  Register^  Fig.  14 

A  cylinder  C,  revolving  with  known  and  uniform  velocity, 
is  enclosed  in  a  box  B^  through  a  groove,  Z>,  in  which  slides  a 
marker  F^  in  contact  with  the  piston  Z. 

The  weight  per  unit  of  the  sectional  area,  ^,  of  (F-Vl^ 
may  be  varied  at  pleasure. 

When  the  gun  is  fired,  a  curve,  such  as  shown,  is  traced 
on  the  cylindery  from  which,  by  finite  differences,  we  have 

^=  -,.  (11) 

^=  ^(KJf  (12) 

8.   T/ie  French  Accelerograph, 

This  projects  vertically  upward  a  piston,  the  mass  of 
which  may  be  greatly  varied  by  the  addition  of  weights. 


16 


VIT. — PRESSURE    GAUGES. 


A  fixed  tuning  fork  traces  the  harmonic  curve  upon  a 
blackened  surface  on  the  piston. 

III.  STATIC  AND  KINETIC  METHODS  COMBINED, 
Objections  to  Kinetic  Method. 

It  will  be  seen  that  the  objection  to  the  kinetic  method 
lies  in  the  liability  of  error  in  the  measurement  of  the  small 
spaces  by  which  the  time  record  is  expressed. 

This  limits  the  method  principally  to  the  cases  where  the 
pressure  changes  but  slowly,  as  in  those  powders  known  as 
slow-burning  powders. 

Noble's  Experiments. 

In  1869,  Capt.  Noble,  R.  A.,  prepared  a  M.  L.  gun  as 
.described,  Chap.  VI.  Crusher  gauges  were  placed  in  the 
holes  leading  to  the  chamber,  and  the  other  holes  were 
provided  with  the  apparatus  also  given  in  Chap.  VI. 

By  observation  and  interpolation,  a  table  of  spaces  and 
times  was  formed  so  as  to  make  A  x  constant=6,  10°^,  as 
follows: 


7J           ^^ 

Av 

/-    ^   a 

X 

/ 

At 

At 

A  V 

logdt 

dt 

^      Ttr^g 

mm. 

sec. 

sec. 

m.  s. 

m.  s. 

* 

m.  s. 

kil.  per 
c=]  cm. 

0.00 
6.10 

0.0000000 
0.0018182 

0.0018182 

8.85 

0.0005590 

7.56 

4.88327 

9891 

271 

12.20 

0.0023772 

10.91 

0.0002528 

9.02 

4.61517 

22082 

005 

18.30 

0.0026330 

19.33 

*  The  values  of  dt  are  obtained  by  interpolation.     That  of  the  mean 


acceleration  for  the  first  value  of    Az^,  viz.,  A/= 


0.0023772 


=0.0011886 


would  evidently  be  too  large,  and  the  corresponding  value  for  /=186.5 
would  be  too  small.  The  method  of  interpolation  is  similar  to  that  here- 
after described  in  Exterior  Ballistics. 


VII. — l-KESSTTRE   GAUGES.  17 

Fig.  15,  represents  the  curves  obtained  in  a  10  in.  gun 
firing  a  300  lbs.  projectile  with  fine  (R.  L.  G.),  and  coarse, 
(Pebble)  powders. 

The  muzzle  velocity  of  the  projectile  was  in  both  cases 
practically  equal. 

Comparison  of  Results. 

The  calculated  pressures  agreed  closely  with  those  ob- 
served in  the  gauges  placed  near  the  base  of  the  projectile 
when  at  rest;  and  those  observed  at  the  base  of  the  bore 
considerably  exceeded  those  observed  near  the  base  of  the 
projectile.    ^^^.  Chap.  XI. 


VIII. — PHENOMENA    OF    CONVERSION. 


CHAPTER    VIIL 

PHENOMENA  OF  CONVERSION. 

Phenomena. 

For  purposes  of  analysis  the  conversion  of  gunpowder 
into  gas  may  be  considered  under  tliree  heads,  viz.:  Ignition^ 
Inflammation  and  Combustion, 
Definitions. 

By  Ignition  is  meant  the  setting  on  fire  of  a  particular 
point  of  a  grain  or  charge. 

By  Inflamination  is  meant  the  spreading  of  the  fire  from 
point  to  point  of  the  surface  of  a  grain,  or  from  one  granu- 
lar surface  to  another  throughout  the  charge. 

By  Combustion  is  meant  the  passage  of  the  inflamed 
surface  throughout  the  substance  of  each  grain. 

IGNITION. 

Gunpowder  is  the  most  refractory  of  the  explosives;  it 
ordinarily  requires  a  temperature  of  300°.  Its  ignitibility 
varies  inversely: 

1st.  With  the  amount  of  moisture  present. 

2d.  With  the  smoothness  and  sphericity  of  the  surface. 

3d.  With  its  density. 

It  also  varies  with  the  character  of  the  charcoal. 

COMBUSTION. 
Definition. 

By  velocity  of  combustion  is  meant  the  rate  of  motion  of 

the  inflamed  surface  in  a  direction  normal  to  that  surface. 

Owing  to  the  impossibility  of  determining  this  within  the 


VIII. — PHENOMENA    OF    CONVERSION. 


gun,    the   velocity   of    combustion   of    different   kinds   of 
powder  in  the  open  air  is  taken  by  the  manufacturer  as  a 
rude  means  of  comparing  their  combustibility. 
Determination. 

If  the  size  of  the  grain  permits  the  time  of  its  burning  to 
be  accurately  determined,  this  simple  method  is  preferred; 
since  it  resembles  most  closely  the  actual  conditions  of  prac- 
tice. Otherwise,  we  may  extend  the  time  to  be  measured 
by  burning,  like  a  candle,  a  prism  of  press  cake  having  its 
sides  greased  to  protect  them  from  the  flame;  or  else,  we 
may  use  a  tube  rammed  with  the  pulverized  mill  cake  of 
the  same  density  as  that  of  the  powder  to  be  tested.  So 
determined,  the  velocity  is  found  to  be  about  0.4  inch  per 
second. 
Nature  of  Combustion.     1.  In  Air. 

This  experiment  proves  that  the  composition  burns  in 
parallel  layers  at  a  uniform  rate;  so  that  the  combustion  of 
a  spherical  grain  would  resemble  the  peeling  of  an  onion. 

This  fact  is  frequently  illustrated  on  the  proving  ground, 
where  burning  grains  of  powder  are  projected  from  the  gun 
with  sufficient  force  to  penetrate  deeply  into  wooden 
boards.  Should  they  fall  in  snow,  their  appearance  will 
plainly  indicate  the  superficial  nature  ot  their  combustion. 
2.  In  Gun. 

It  is  important  to  remember  that  the  velocity  of  combus- 
tion within  the  gun  is  very  much  greater  and  less  uniform 
than  that  in  the  open  air.  The  process  resembles  roughly 
the  absorption  of  water  by  a  porous  substance  when  under 
variable  hydrostatic  pressure.  The  effect  may  be,  not  only 
to  accelerate  the  velocity  of  combustion,  but  also,  by  break- 
ing up  the  grains,  to  increase  the  burning  surface;  as  we 
crush  sugar  to  facilitate  its  solution. 

The  velocity  of  combustion  is  supposed  to  vary  directly 
with  the  intensity  of  the  gaseous  pressure. 


VIII. — PHEKOMENA   OF   CONVERSION. 


CIRCUMSTANCES  AFFECTING    THE  VELOCITY  OF    COMBUSTION 

IN    AIR. 

Varying  Conditions. 

Under  similar  circumstances  the  velocity  of  combustion 
of  homogeneous  powder  is  constant.  It  varies  however, 
with  the  purity^  proportions^  incorporation^  density  and  con- 
dition of  the  powder  as  follows; 

1.  Purity. 

The  nitre  and  sulphur  should  be  pure,  or  nearly  so.  The 
part  that  charcoal  plays  depends  upon  its  combustibility. 
This  is  determined  by  finding  the  velocity  of  its  combus- 
tion, when  incorporated  with  a  due  proportion  of  nitre  in 
such  a  tube  as  above  described. 

2.  Proportions. 

By  varying  the  proportions,  all  velocities  up  to  0.55  inch 
per  second  can  be  obtained. 

The  proportions  usually  adopted  are  those  that  give  the 
greatest  volume  of  gas  in  a  given  time,  because  the  mass 
burned  is  the  greatest,  and  because  each  unit  of  mass  gives 
the  greatest  volume  of  gas. 

3.  Incorporation. 

Prolonging  the  incorporation  increases  the  velocity  at  a 
rate  which  increases  as  the  proportions  approach  those 
adopted. 

4.  Density. 

With  each  set  of  proportions  a  density  is  soon  reached 
that  corresponds  to  the  maximum  velocity.  Beyond  this 
density  the  velocity  varies  inversely  as  the  density,  at  a  rate 
which  increases  as  the  proportions  approach  those  adopted. 

The  increase  in  superficial  density  due  to  glazing  dimin- 
ishes the  velocity  of  combustion;  provided  that  the  dust 
formed  in  the  process  be  removed. 


VlII. — PHENOMENA    OF   CONVERSION. 


5.  Condition. 

The  velocity  increases  with  the  porosity  of  the  powder. 
See  page  2.  The  porosity  may  result  from  the  evaporation 
of  water,  alcohol,  or  vinegar,  added  to  the  substance  before 
pressing  it.  When  porosity  is  carried  to  the  point  of  fria- 
bility, the  consequences  described,  page  2,  may  be  expected. 

AVhen  oils,  gums,  or  resins  are  added,  or  when  an  excess 
of  water  remains  in  the  composition,  the  velocity  of  com- 
bustion is  diminished.  An  excess  of  water  permits  the  nitre 
to  segregate  and  to  neutralize  the  effects  of  incorporation. 

Re7nark< 

These  variations  should  be  carefully   studied,  as  upon 
them  depend  the  most  important  characteristics  of  gun- 
powder. 
Emergency  Powder. 

For  example;  during  the  Franco-German  War  of  1870,  it 
was  found  necessary  to  increase,  far  above  their  normal 
capacity,  the  product  of  the  powder  mills  remaining  in  the 
hands  of  the  French. 

This  was  accomplished  by  reducing  the  time  of  incor- 
poration under  the  wheels,  besides  calling  into  use  the  stamp 
mills  and  rolling  barrels  formerly  employed  for  this  pur- 
pose. 

The  effect  of  less  thorough  incorporation  upon  the 
velocity  of  combustion  was  neutralized  by  reducing  the 
density  of  the  powder. 

This  answered  well  where  the  powder  was  not  intended 
to  be  stored,  and  where  the  capacity  of  the  chambers  in 
which  it  was  to  be  fired  permitted  a  corresponding  increase 
in  the  volume  of  the  charge. 

The  differences  of  the  effects  upon  the  gun  and  its  pro- 
jectile, resulting  from  varying  the  phenomena  of  combus- 
tion, are  described  in  Chapters  X  and  XI. 


VIII, — PHENOMENA    OF    CONVERSION. 


INFLAMMATION. 
Hypothesis. 

The  inflammation  of  a  single  grain  is  generally  assumed 
to  be  instantaneous,  and  so  is  that  of  a  charge  of  powder; 
unless  the  time  of  its  inflammation  bears  so  considerable  a 
ratio  to  that  of  its  combustion  that  the  total  time  required 
for  the  conversion  of  the  charge  into  gas  is  sensibly  in- 
creased. 

Experiment. 

The  nature  of  the  process  may  be  studied  by  determining 
the  time  required  to  inflame  trains  of  powder  of  known 
lengths  under  various  conditions. 

Varying  Conditions. 

The  velocity  of  inflammation  is  found  to  vary: 

1.  With  the  disposition  of  surrounding  bodies. 

2.  With  the  size  and  shape  of  the  grains. 

3.  With  their  composition  and  constitution. 

1.  Confinement. 

The  heated  gases,  evolved  by  ignition,  follow  in  their  ex- 
pansion the  line  of  least  resistance.  If  they  are  confined, 
so  that  this  line  coincides  with  that  along  which  the  powder 
is  disposed,  its  rate  of  inflammation  is  increased.  Thus,  the 
velocity  of  inflammation  of  a  train  is  increased  by  firing  it 
in  a  tube  instead  of  in  the  open  air.  It  is  still  further 
increased  when  the  cross-section  of  the  tube  is  not  entirely 
filled;  and  when  the  bottom  of  the  tube,  near  which  the 
train  is  ignited,  is  closed,  as  in  a  gun. 

2.  Size  and  Shape  of  Grain. 

The  size  and  shape  of  the  grain  affect  both  the  force 
propelling  the  gases  and  the  resistances  which  they  encoun- 
ter. In  the  first  case,  the  size  and  shape  of  the  grain  affect 
the  amount  of  gas  evolved  in  equal  successive  times  and 
also  the  ignitibility  of  the  unburned  grain;  in  the  second 


VIII. — PHENOMENA   OF    CONVERSION. 


case,  they  affect  the  size  and  shape  of  the  spaces  between 
the  grains.  So  that,  in  fine  powder,  although  the  gaseous 
pressure  may  be  greater,  the  resistance  to  the  passage  of  the 
wave  of  inflammation  may  also  be  greater.  In  coarse  pow- 
der the  converse  may  be  the  case.  The  velocity  of  inflam- 
mation should  therefore  be  determined  by  experiment. 

It  is  now  much  less  important  than  when  muzzle  loading 
guns  were  in  use. 

If  the  charge  be  made  of  mealed  powder  compressed, 
there  will  be  no  interstices;  and  the  velocity  of  inflammation 
and  that  of  combustion  will  be  the  same. 

If  it  be  of  concrete  powder,  the  velocity  of  combustion  of 
the  entire  grain  will  be  that  of  the  inflammation  of  the  con- 
stituent grains,  and  will  be  greater  than  that  of  the  com- 
pressed mealed  powder  above  referred  to. 

This  ratio  was  found  to  be  as  1.4  to  1.0. 
3.  Composition  and  Constitution. 

The  velocity  of  inflammation  is  affected  by  variations 
in  the  purity  and  proportions  of  the  ingredients,  in  the 
thoroughness  of  their  incorporation,  and  in  the  density  of 
the  powder,  in  so  far  as  these  affect  its  velocity  of  combus- 
tion and  its  susceptibility  to  ignition. 


IX. — NOBLE    AND    ABEL's    EXPERIMENTS. 


CHAPTER  IX. 

NOBLE  AND  ABEL'S  EXPERIMENTS. 

From  1868  to  1874,  Captain  Noble,  R.  A.,  and  Mr.  F.  Abel, 
the  chemist  of  the  British  War  Department,  made  a  series 
cf  experiments  upon  gunpowder  that  have  become  his- 
torical. 

NATURE  OF  THE  EXPERIMENTS. 

These  experiments  were  conducted  on  the  principle, 
general  in  all  experimental  comparisons,  of  keepmg  all  con- 
ditions constant  except  that  of  the  variable  under  consideration. 

Although  their  ultimate  object  was  to  determine  the 
behavior  of  fired  gunpowder  in  the  variable  volume  behind 
the  projectile  in  a  gun,  this  principle  required  that  their 
preliminary  experiments  should  be  conducted  in  closed 
vessels,  the  capacity  of  which  was  invariable  and  accurately 
known. 

VARIABLES. 

They  accordingly  varied: — 

1.  The  composition  of  the  powder. 

2.  The  size  of  its  grain. 

3.  The  mass  of  gunpowder  exploded  in  a  given  volume, 
or  the  density  of  loading. 

FUNCTIONS. 

Under  these  different  circumstances  they  observed: — 

1.  The  maximum  pressures  per  unit  of  area. 

2.  The  composition  and  condition  of  the  products  of 
combustion. 


2  IX. — NOBLE   AND   ABEL's   EXPERIMENTS. 

3.  The  specific  volume  of  the  gases  formed,  viz^  at  a 
pressure  of  one  atmosphere  and  at  0°. 

4.  The  quantity  of  heat  evolved  by  the  combustion. 

CONCLUSIONS. 

From  the  observed  states  of  the  functions  corresponding 
to  particular  values  of  each  variable  they  sought  to 
determine  the  law  expressing  the  relation  between  pres- 
sures, volumes  and  temperatures  in  closed  vessels,  with  the 
view  of  applying  it  to  the  variable  conditions  existing  in 
guns. 

METHODS   FOLLOWED   IN  THE  EXPERIMENTS. 

VARIABLES. 

1.  Composition  of  Powders. 

Four  of  the  six  kinds  of  powders  tried  were  approxi- 
mately of  the  usual  composition.  The  others  differed 
notably  as  seen  by  the  following  table: 

COMPONENTS.  POWDERS. 

Four  English.     Spanish.     Blasting, 

Nitre,  74 

Carbon,  12 

Sulphur,  10 

Water,  H,  O,  Ash,  etc.,  4 

100        100        100 

2.  Size  of  Grain. 

The  principal  experiments  in  which  the  size  of  grain 
entered  as  a  variable  were  those  in  which  comparisons 
were  made  between  R.  L.  G.  (Rifle,  large  grain)  and  the 
Pebble  powders  referred  to  Chap.  VII.  The  linear  dimen- 
sions of  these  powders  were  about  as  1  to  3. 

3.  Density. 

It  is  evident  that  the  results  of  the  experiments  were 
largely  dependent  upon  the  relation  existing  between  the 


75 

62 

9 

18 

12 

15 

4 

5 

!X. — NOBLE   AND   ABEL's   EXPERIMENTS. 


mass  of  the  charges  and  the  volumes  in  which  they  were 
fired.  This  requires  a  discussion  of  the  density  of  powder 
which  is  named  under  three  heads. 

1.  Specific  Gravity. 

By  density  simply,  or  d,  we  mean  the  specific  gravity  of 
the  press-cake,  or  that  of  the  individual  grains,  referred  to 
water.  This  in  practice  ranges  from  1.68  to  1.85.  The 
maximum  attainable  density  calculated  from  that  of  the 
ingredients  of  gunpowder  united  in  their  ordinary  propor- 
tions, is  1.95. 

2.   Gravimetric  Density. 

By  this  term,  or  y^  we  mean  the  density  referred  to  water 
of  grained  powder,  including  its  interstitial  volumes;  or, 
calling  w,  the  weight  in  pounds  of  one  cubic  foot  of  the 
loose  powder. 

^~  62.425  ^^ 

The  gravimetric  density  is  sometimes  expressed  by  the 
weight  in  ounces  of  one  cubic  foot  of  the  loose  powder. 

The  gravimetric  density  of  powder  is  important  when  it 
is  to  be  used  in  a  limited  'volume  as  in  the  cartridges  for 
breech-loading  small  arms  and  in  explosive  projectiles.  It 
is  evident  that  the  form  of  grain  and  the  amount  of  settling 
affect  the  interstitial  volumes  and  hence  its  value.  For 
loosely  piled  powder  of  irregular  granulation  it  is  about  0.9. 

Specific  and  Interstitial  Volumes. 

The  amount  of  the  interstitial  volumes,  which,  as  seen  in 
Chap.  VIII,  affects  the  rate  of  inflammation,  may  be  de- 
termined as  follows: 

Let  F,  represent  the  volume  of  the  powder  when  loose; 
v,^  its  specific  volume,  or  its  volume  when  compressed  to  a 
uniform  density,  6 ;  and  v' ^  the  sum  of  the  interstitial  volumes : 
then,  since  w  =  F  y  =  z^,  (5. 


IX. — NOBLE    AND    ABEL  S   EXPERIMENTS. 


d  :  y  ::  V  W  or    v=y  -k-  (2) 

whence  v'=  F-v=  F^^"^^  (3) 

Ordinarily,  d  is  about  1.8;  and,  when  the  powder  is  loosely 

y 
piled,  V  is  about  0.9.    In  such  a  case  v=v^=  -^. 

Noble  conducted  his  experiments  with  powder  so  closely 
packed  that  y  was  sometimes  equal  to  unity:  in  such  a  case 
v'  was  sensibly  equal  to  0.44  F. 

3.    Density  of  Loading. 

By  this  term,  or  A ,  we  express  the  relation  between  the 
mass  of  a  charge  of  powder  and  the  volume  in  which  it  is 
fired. 

If  the  values  of  S  and  y  were  constant,  it  would  suffice  to 
say  that  the  cavity  holding  the  powder  was,  say,  one-half, 
three-quarters  full,  etc.  This  was  the  method  adopted  by 
the  early  experimenters. 

But  the  quantity  of  matter  in  a  given  volume  of  grained 
powder  may  vary  from  both  the  causes  named. 

The  value  of  A  is  therefore  taken  as  the  ratio  of  the 
weight  of  the  powder  fired,  to  the  weight  of  water  at  its 
maximum  density  which  would  fill  the  volume  in  which  the 
powder  is  fired.  Calling  this  volume  expressed  in  cubic 
feet   F,  and  expressing  w^  as  before,  in  pounds,  we  have 

w 
^  ^   Fx  62.425  (^^ 

It  is  usual  to  give  the  linear  dimensions  of  guns  in 
mches;  therefore  calling  z;=  Fx  1728,  the  volume  in  cubic 
inches,  we  have 

•  ,^^^  (5) 

This  value  of  A  is  of  constant  application  and  must  be 
remembered. 


IX. — NOBLE   AND    ABEL's   EXPERIMENTS. 


APPARATUS. 

The  vessels  employed  were  strong  steel  cylinders  as 
shown  in  Fig.  1.  Each  one  contained  a  firing  plug,  F^  with 
a  conical  stopper,  /,  insulated  from  7^  by  a  washer,  w,  and  by 
sheet  of  tissue  paper  wrapped  around  its  body.  Another 
conical  screw  plug,  P,  carried  a  crusher  gauge,  C. 

The  object  of  the  form  given  to  F  and  P  was  to  facilitate 
their  removal;  since  a  very  slight  motion  would  free  them 
from  the  walls. 

The  charge  was  ignited  by  an  electric  igniter,  /. 

After  the  firing  the  vessel  was  immediately  conveyed  to  a 
calorimeter;  or  a  smaller  vessel.  Fig.  2,  could  be  fired 
under  water. 

FUNCTIONS. 

1.  Pressures. 

These  were  determined  by  the  crusher  gauge,  and  the 
observed  results  compared  and  corrected  by  the  methods 
used  in  experimental  research. 

2.  Nature  of  Products. 

Small  samples  of  gas  were  drawn  off  for  analysis  through 
the  tube,  E,  opened  by  slightly  unscrewing  the  valve  e. 

The  initial  liquidity  of  the  non-gaseous  products  was 
determined  by  tipping  the  cylinder  in  various  directions 
soon  after  the  explosion,  and  by  observing  the  appearance 
of  the  solid  crust  when  the  vessel  was  finally  opened. 

3.  Volume  of  Gases. 

The  specific  volume  of  the  gases  was  determined  by  a 
gasometer.  Fig.  3.  The  long  wTench,  w,  passing  through 
the  stufhng-box,  sb^  was  used  to  unscrew  P^  immediately 
after  the  explosion. 

4.  Heat. 

The  quantity  of  heat  evolved  by  the  conversion  was 
determined  by  immersing  the  vessel  in  a  calorimeter  con- 


6  IX. — NOBLE    AND    ABEL'S   EXPERIMENTS. 

taining  a  known  weight  of  water  of  known  temperature, 
and  by  noting  the  resulting  rise  in  temperature. 

RESULTS  OF  THE   EXPERIMENTS. 

STATES   OF    THE    FUNCTIONS. 

1.  Pressures. 

For  all  kinds  and  sizes  of  powder  the  pressure  was  found 
to  be  practically  constant  for  equal  densities  of  loading,  or 
the  force  o(  SiW  the  powders  was  the  same.  When  A=l, 
the  force  was  about  6,400  atmospheres,  or  43  tons,  or 
96,000  lbs.,  per  square  inch. 

2.  Products. 

The  following  table*  gives,  by  weight  per  cent,  the  mean 
proportions  of  the  products  resulting  from  many  experiments; 

PRODUCTS.  KINDS  OF  POWDER. 

Gaseous.  Tour  English.    Spanish.    Blasting. 

CO2, 

CO, 

N, 
Various, 

Total  Gaseous, 

Non-Gaseous. 

K,  CO3, 
K2SO4, 
Ka  S, 
Various, 

Total  Non-Gaseous,  66  62  49 

From  the  appearance  of  the  cavity  after  firing,  the  non- 
gaseous products  were  supposed  to  be  suspended  at  the 
instant  of  the  explosion  as  a  highly  heated  liquid  spray 
which  eventually  assumed  a  solid  form.     In  cooling  it  was 


26 

25 

23 

3 

1 

15 

11 

11 

9 

4 

1 

4 

44 

38 

51 

34 

22 

19 

12 

30 

6 

6 

17 

4 

5 

13 

*NoTE. — The  relative  proportions  of  the  total  gaseous  products  and  of 
CO,  should  be  learned.    See  Chapter  II, 


IX.- 


supposed  to  shrink  from  about  0.6  the  volume  of  the  entire 
charge,  or  0.6  F,  page  3,  to  about  0.3  V. 

Confining  our  attention  to  the  typical  English  powders  it 
is  significant  to  observe  that  very  nearly  the  same  propor- 
tions were  concluded  to  exist  between  the  volumes  occu- 
pied by  the  gaseous  and  non-gaseous  products  at  the  instant 
of  the  explosion,  as  were  found  to  exist  between  the  weights 
of  these  products  and  between  the  interstitial  and  specific 
volumes  of  the  charge. 

That  the  non-gaseous  products  did  not,  by  their  volati- 
lization, augment  the  volume  of  the  gases  was  inferred  from 
their  behavior  when  exposed,  solid,  in  a  Siemen's  furnace, 
to  a  temperature  of  about  1700°.  At  this  temperature 
which,  although  the  highest  available,  was  about  700°  lower 
than  that  determined  by  calculation,  the  solids  swelled  to 
nearly  twice  their  volume,  but  did  not  volatilize. 

3.  Volumes.     4.  Heat.  ^ 

The  relations  between  the  specific  volumes  of  the  gases 
and  the  calorific  values  of  the  powders  appear  from  the 
following  table  which  illustrates  the  curious  fact,  noted  in 
Chap.  II,  that  their  product  is  approximately  a  constant 
quantity.  The  volumes  are  referred  to  that  occupied  by  tlie 
powder  when  A  =  1.     See  note  1,  page  13. 

Kind  of  Powder.        Specific  Volumes.  Heat  Units  Products, 

or  vq.  or  H. 

English  powders,  264  737  194568 

Spanish  powder,,  234  767  179478 

Blasting  powder,  360  517  186120 

Had  the  experimenters  known  the  specific  heat  of  the 

products  of  combustion  when  at  a  constant  volume,  or  C^, 

the  absolute  temperature  of  the  conversion,  or  Tq,  might 

have  been  determined  from  the  general  equation, 

If 


IX. — NOBLE    ANt)    ABEL*S   EXPERIMENTS. 


but,  although  the  same  products  were  always  formed,  they 
occurred  in  such  varying  proportions,  even  when  all  the 
conditions  were  as  nearly  as  possible  identical,  that  no 
certain  conclusions  could  be  made.     Chap.  II,  page  7. 

Also,  by  taking  the  mean  specific  heats  of  the  mean  of 
the  non-gaseous  products,  when  in  a  solid  form,  and  also  of 
the  gases,  a  temperature  was  computed  which  was  mani- 
festly too  great.  The  experimenters  accordingly  adopted 
the  following  course  in  which  the  deductions  of  theory  are 
corrected  by  experiment. 

Temperature  of  Explosion. 

Assuming  the  general  equation  for  the  work  of  perma- 
nent gases  subjected  to  changes  in  temperature,  or — 

pv=^rt,  (6) 

in  which  r  is  a  constant,  and  t  is  reckoned  from  absolute 
zero;  let  us  express/  in  atmospheres. 

The  preceding  table  gives  for  the  English  powders  a 
mean  value  of  r=  (264  =  v)  (1  =/)  v  (273  =  /)  =  0.967. 

Substituting  the  values  of  v  and  /  for  A  zz:  1,  we  have — 
/=  (6400)  (0.4)  ^  0.967  =  2646°  absolute,  =  2373°  C 

This  was  verified  for  varying  values  of  A  and  by  the  ex- 
posure to  the  temperature  of  the  explosion  of  very  fine 
platinum  wire  which  melts  at  about  the  temperature  above 
determined. 

CONCLUSIONS. 
Fundamental  Hypothesis. 

The  remarkable  compensation  between  the  volumes  of 
gas  generated  and  heat  evolved  permitted  Noble  and  Abel 
to  apply  to  these  gases  the  laws  of  Mariotteand  Gay-Lussac; 
provided,  that  from  the  volume  of  the  chamber  in  which  the 
explosio7i  occurred  was  subtracted  the  volume  occupied  by  the 
non-gaseous  residue. 


IX. — NOBLE    AND    AP>EL  S   EXPERIMENTS.  9 

Remarks. 

This  conclusion,  although  simplifying  the  labors  of  the 
experimenters,  and  useful  for  a  general  discussion  like  the 
present,  is  now  believed  to  depend  upon  a  compensation  of 
errors. 

It  is  now  believed  that  the  solid  products  are  volatilized 
and  probably  dissociated,  and  it  is  known  that  Mariotte's 
law  does  not  apply  to  the  pressures  observed  in  guns. 

Still  the  latest  researches  lead  to  practically  the  same  con- 
clusions reached  by  these  experimenters. 

EXPERIMENTS  IN  GUNS. 

The  experimenters  found  that  when  the  gases  expanded 
into  a  varying  volume,  as  in  the  gun,  results  similar  to  those 
above  described  were  found,  vk.: 

1.  Products. 

That  the  nature  and  proportions  of  the  products  remained 
the  same  as  in  a  closed  vessel. 

2.  Working  Substance. 

That  the  work  on  the  projectile  may  be  considered  to  be 
due  to  the  elastic  force  of  the  permanent  gases. 

3.  Source  of  Energy. 

That  the  heat  evolved  by  the  non-gaseous  residue  main- 
tains the  gases  at  a  constant  temperature  during  their  expan- 
sion, which,  therefore,  is  isothermal. 

This  is  essentially  the  hypothesis  of  Hutton,  made  a  cen- 
tury ago.  For  want  of  suitable  apparatus  Hutton  erred 
greatly  in  his  deductions  from  this  hypothesis, 

4.  Theoretical  Work. 

The  total  theoretical  work  of  the  permanent  gases,  when 
indefinitely  expanded,  was  computed  to  be  about  486  toot- 
tons  per  pound  of  powder. 


10  IX. NOBLE    AND    ABEL's    EXPERIMENTS. 

This  is  nearly  the  result  given  by  the  table  on  page  7. 
Only  from  13  to  20  per  cent,  of  this  work  can  be  realized 
in  practice.     See  note  2,  page  13. 
6.  Loss  of  Heat  by  Absorption. 

The  quantity  of  heat  lost  by  absorption  was  approxi- 
mately determined  by  plunging  into  a  calorimeter  a  field 
piece,  after  firing  from  it  a  number  of  rounds  in  rapid  suc- 
cession. 

The  loss  was  found  to  vary  directly  with  the  ratio  of  the 
cooling  surface  to  the  weight  of  the  charge,  and  also  with 
the  time  of  travel  in  the  bore. 

It  varied,  per  unit  of  weight  of  the  powder  fired,  approx- 
imately as  follows: 

Gun.  Loss  in  H.         ^  Energy. 

10  in.  M.  L.  R.  25  3.5 

12  pdr.  B.  L.  R.  100  14.0 

0.45  in.  B.  L.  R.  musket'        250  35.0 

6.  Pressures. 

The  experimenters  confined  themselves  to  the  prediction 
of  velocities.  The  determination  of  the  actual  intensity  of 
the  variable  pressure  during  the  progressive  combustion  of 
the  powder  in  a  volume  varying  with  the  position  of  the  pro- 
jectile during  combustion  was  determined  in  only  a  few 
special  cases.  The  important  law  by  which  this  pressure 
varies,  upon  which  modern  guns  are  constructed,  was  left 
unsolved. 

The  methods  of  M.  Emil  vSarrau,  of  the  ^'-  D^partement 
des  Poudres  et  Salpltres^''  which  depend  rather  upon  dynam- 
ical than  chemical  laws,  corrected,  like  those  of  Noble  and 
Abel,  by  experiment,  are  now  generally  followed  where  ac- 
curate prevision,  both  of  pressures  and  velocities,  is  required. 

The  older  methods  are  adopted  in  this  text,  as  they  permit 
the  presentation  of  some  of  the  more  important  phenomena 
of  fired  gunpowder  in  a  relatively  simple  form. 


IX. — NOBLE    AND    ABEL's   EXPERIMENTS.  11 


DEDUCTION  OF   THE   VARIABLE   PRESSURES   IN  A 

GUN. 
Hypothesis. 

It  has  been  shown  in  Chapter  VIII.  that  the  conversion 
of  gunpowder  is  not  instantaneous.  Yet,  on  account  of  the 
difficulty  of  determining  the  circumstances  of  the  motion  of 
the  projectile  during  the  period  of  combustion,  or  x=q)  (t) 
and  the  rate  of  combustion  under  the  varying  pressure  to 
which  the  powder  is  exposed,  or  gz=/  (t)  it  is  best  to  begin 
by  assuming  that  the  conversion  is  instantaneous,  and  to  cor- 
rect the  results  of  computation  by  experiment.  See  note  3, 
page  13. 

Assuming  then,  the  proportions  of  solid  and  gaseous  pro- 
ducts previously  given,  and  that  the  change  in  pressure  is 
due  to  the  change  in  volume  in  rear  of  the  projectile  (which, 
under  the  isothermal  hypothesis,  acts  like  a  piston  moving 
with  variable  velocity  under  some  external  force),  we  may 
deduce  the  following  relation  between  the  pressure  and  the 
mean  density  of  the  products  of  the  explosion. 

Let  /  represent  the  intensity  of  the  gaseous  pressure  in 
tons  per  square  inch,  and 

Wy  the  weight  of  the  charge  in  pounds; 

Vf  the  variable  volume  behind  the  projectile  in  cubic 
inches; 

v'f  the  volume  occupied  by  the  non-gaseous  products  in 
cubic  inches; 

<^,  the  density  of  these  products  referred  to  water; 

d,  the  density  of  the  gases  referred  to  water  and  supposed 
to  remain  at  a  constant  temperature. 

jff,  the  ratio  -^  assumed  under  Mariotte's  law  to  be  con- 
stant. 

Deduction. 

From  the  general  expression  for  density  we  have 


12  IX. — NOBLE    AND    ABEL's   EXPERIMENTS. 


^     0.44  wx  27.68      12.18  a/  , 

d— -. = -J-  ;  and 

v—v  v—v 

^,     0.56  wx  27.68        ,      \h.hw 

d'^ -, •••^^--^7-;   and 


^  15.5  w 

" — n^' 

Multiplying  both  numerator  and  denominator  of  the  value 
of/  by 

27.68         2.2724 


12.18  z;~       V 


,  we  have 


p=R ^ -.  (7) 

2.2724-1.2726  -^ 

The  ratio,  R^  is  found,  by  experiment,  not  to  be  absolutely 
constant;  but,  by  selecting  from  Noble's  experiments  in 
closed  vessels,  suitable  values  of  /  and  A  in  pairs,  and  by 
substituting  these  values  in  Eq.  (7),  we  may  obtain  two 
equations,  containing  two  unknown  quantities,  from  which 
we  find   (See  note  4,  page  13.) 

7?=32.18  ^'=0.824. 

These  values  substituted  in  Eq.  (7)  give,  after  reduction, 
_  1  * 

A 
Which,  for  convenience,  may  be  placed  under  the  form 

/= 1  (9) 

0.0025571  -  -0.048 

w 

Equations  (8)  and  (9)  give  remarkably  close  approxi- 
mations to  all  but  the  very  highest  pressures  found  in  Noble's 
experiments  in  closed  vessels. 

*log  0.070618  ="3.8489170.         flog  0.0025571  =  3^4077557. 


IX.— NOBLE   AND   ABEL's   EXPER1M£NTS.  13 


COROLLARIES. 

V 

1.  By  substituting  in  Eq.  (9)  proper  values  for  ^=  — ^>we 

may  construct  a  curve,  as  in  fig.  4,  which  will  give  the  pres- 
sures at  different  points  along  the  bore  of  the  gun  under  the 
assumptions  noted,  page  11. 

Should  the  piece  be  chambered,  the  value  of  x\  the  re- 
duced length  of  the  chamber  =.Yo\vimQ.  of  chamber-^  ;r  t^  must 
replace  its  measured  length. 

2.  It  is  evident  that  the  value  of  the  initial  ordinate  is 
determined  by  the  value  of  the  density  of  loading,  A. 

3.  Also  that,  knowing  by  experiment  the  intensity  of  the 
maximum  pressure,  and  the  charge,  we  may  determine 
approximately  the  corresponding  position  of  the  projectile. 

__  ^  [l+(/X  0.048)1 
Smce  X  —     ^^py^  0.0025571  ' 

4.  Also  that  we  may  determine  the  charge  required  to 
burst  a  closed  vessel,  like  an  explosive  projectile,  when  its 
resistance  to  rupture  is  known. 

NOTES. 

1.  Page  13. — The  experimenters  ascertained  that  the  erosion  of  the 
bore,  caused  by  the  rush  of  the  gases  past  the  projectile,  increases  directly 
with  the  factor  H,  and  inversely  with  v^. 

Since  modern  steel  guns  fail  rather  from  erosion  than  from  bursting,  it 
is  possible  that  the  large  values  of  H,  now  generally  sought,  may  be 
ultimately  diminished  in  favor  of  z/q. 

That  is,  that  the  guns  have  a  surplus  of  strength  that  may  profitably 
be  used  to  favor  their  endurance  under  erosion. 

2.  Page  10.— Taking  y=1390  ft. -lbs.  for  !«  C  we  have 
Q=-U[=  '^^TXISQO  ^  ^g,^  3  Qj.  94         ^^^^^  oi4:%Q.  foot  tons. 

2240  2240 

3.  Page  11.  X  and  a  signify  respectively  the  variable  space  passed 
over  by  the  projectile  and  the  variable  surface  of  the  burning  grains  com- 
posing the  charge.     Chap.  XI,  pp.  2,  3,  4. 

4.  Page  12. — For  recitation  at  the  board  the  numerical  values  after 
Eq.  (7)  may  be  represented  by  symbols. 


X.— eoMStrstiON    IN  Alft. 


CHAPTER    X. 

COMBUSTION  IN  AIR. 

Single  Grain. 

We  know  from  the  experiment  in  Chap.  VIII  that  in  air, 
gunpowder  burns  only  superficially,  so  that  the  burning 
under  these  circumstances  of  a  spherical  grain  may  be 
likened  to  the  exceedingly  rapid  peeling  of  an  onion. 

Considering,  for  the  present,  all  solid  grains  to  be  repre- 
sented by  their  equivalent  spheres,  the  radius  of  any  sphere 
will  be  equally  shortened  in  equal  successive  times,  but  the 
surface  and  the  volume  will  vary  in  a  higher  ratio  to  the 
time. 

Accordingly  let  Fig.  1  represent  the  central  section  of 
a  hom.ogeneous  spherical  grain  burning  with  a  uniform 
velocity  of  combustion  which  in  the  variable  time,  /,  will 
reduce  the  original  radius  R,  to  r,  and  the  original  surface 
iS",  to  s.  Let  the  time  required  for  the  combustion  of  the 
entire  grain  be  r. 

Then  ^:  j::i?2 :  ;^::t2  :  (r-/)2,  or 

^=^{r-t)\  (1) 

By  differentiating  Eq.  (1)  with  respect  to  s  and  /  we  have 

It  may  be  shown  from  Equations  (1)  and  (2)  that  the 
curve,  Fig.  2,  expressing  the  relation  s=/{f),  is  a  parabola 
referred  to  a  system  of  rectangular  axes;  one  of  which,  the 
axis  of  times,  coincides  with  the  tangent  at  the  vertex  of  the 
parabola,  and  has  upon  it  the  origin,  O,  at  a  distance  from 
the  vertex =r. 


X. — COMBUSTION     IN    AIR. 


The  rate  of  change  of  the  ordinate  of  the  curve  is  the 
same  as  that  of  the  surface  of  the  burning  grain. 

The  summation  of  the  successive  ordinates  of  the  curve, 
corresponding  to  any  value,  /,  will  be  equal  to  the  area 
O  Ssf;  and  since  the  ordinates  represent  the  correspond- 
ing successive  surfaces,  this  area  will  be  proportional,  either 
to  the  mass  or  volume  of  the  grain  which  has  been  burned 
up  to  the  time  /,  according  as  the  density  of  the  powder  is, 
or  is  not  considered. 

y''        dw 
sdtj-j-  =s,  or  the  rate  at 

which  the  mass  of  gas  is  increasing  at  any  instant,or  the 
rate  of  conversion,  is  proportional  to  the  corresponding 
surface.* 

The  total  area  O  S  r=  — - —  will  be  proportional  to  the 

o 

original  mass  or  volume  of  the  grain. 
Number  of  Grains  Varied. 

Such  a  relation,  once  established,  would  be  true  for  all 
equal  grains  composing  a  charge,  and  would  therefore  be 
true  for  the  whole  charge,  but  the  rate  of  conversion  would 
vary  with  the  size  of  the  charge  as  shown  by  curves  1  and 
2,  Fig.  3.  In  these,  1,  represents  such  a  curve  as  shown  in 
Fig.  2,  for  a  single  grain;  and  2,  the  same  for  n  grains  com- 
posing a  charge. 
Size  of  Grains  Varied. 

If,  in  a  charge  of  a  given  weight  composed  of  spherical 
grains  of  a  given  density,  the  -size  only,  of  the  grains  be  in- 


*If  the  grain  be  not  homogeneous,  and  burn  with  a  variable  velocity 
the  rate  of  conversion  will  vary  with  the  product  of  the  surface,  J,  of  the 
density,  b,  and  of  the  velocity  of  combustion  ft),  or 

=  J  X  0  X  w. 

dt 

In  this  case  the  curve  will  no  longer  be  a  parabola, 


X. — COMBUSTION    IN    AIR. 


creased,  the  sum  of  the  granular  surfaces,  ^  S,  will  be  in- 
versely proportional  to  the  radius  of  the  grain. 

•For  W=n  v  d,  and  v=  — jr—  .-.  W= 


or^= 


3  3      ' 

3  W        1^ 

nS  '      r 

or         r 

If  we  represent  by  ^  the  sum  of  the  initial  granular 
surfaces  of  a  charge,  and  by  6  the  sum  of  the  successive 
granular  surfaces  of  the  same  charge  during  its  combustion; 
Fig.  4  may  represent  by  curves  1  and  2,  respectively,  the 
relation  G=f  {f)  for  charges  of  equal  weights  composed  of 
grains  of  different  sizes. 
Objections  to  increasing  Size  of  Grain. 

The  effect  of  increasing  the  size  of  the  grain  is  to  make 
the  powder  relatively  slow  ;  or,  as  it  is  called  with  reference 
to  its  action  in  the  gun,  7nild  or  progressive.    This  diminishes 

the  value  of  --z-  by  increasing  the  value  of  r. 

The  objection  to  this  will  hereafter  appear;  it  will  suffice 
here  to  say  that  it  may  require  the  gun  to  be  of  inconvenient 
length. 

Alternatives. 

The  following  methods  have  been  proposed  for  regulating 
the  rate  of  conversion  without,  in  all  cases,  increasing  the 
value  of  r. 
Constant  Rate. 

1.  A  constant  rate  would  evidently  be  attained  by  form- 
ing the  powder  as  a  prism  and  confining  the  burning  area  to 
that  of  its  cross  section.  This  result  is  approached  in  the 
Zalinski  pneumatic  gun,  in  which  compressed  air  from  a 
large  reservoir,  expands  continuously  into  the  volume  be- 
hind the  projectile.     Also  in  the  steam  engine. 


X. — COMBUSTION     IN    AIR. 


2.  An  approximation  to  a  constant  rate,  with  a  small  value 
of  r,  has  been  sought  by  forming  the  powder  into  volumes 
of  which  two  dimensions  considerably  exceed  the  ihird.  The 
French,  Castan,  powder  and  the  American,  LX,  powder  are 
so  formed. 

Increasing  Eate. 

The  rate  of  conversion  may  be  increased  by  causing  the 
burning  surface  to  increase: 

3.  By  igniting  the  grain  from  the  interior,  and  protecting 
the  exterior  surface  from  the  flame  by  forming  the  grains 
into  hexagonal  prisms  closely  packed  together,  fig.  5.  The 
perforations  are  continuous  flues,  facilitating  inflammation. 

This  is  Rodman's  powder. 

4.  By  diminishing  the  density  of  the  grain  toward  its 
center,  Chap.  III.,  or  by  facilitating  its  disruption  after 
ignition. 

These  cases  may  be  represented  by  the  correspondingly 
numbered  lines  on  figure  6. 

COROLLARY. 

Supposing  the  charge  to  consist  of  n  equal  spherical  grains, 
the  proportion  of  the  whole  charge  that  will  be  burned  in  the 
variable  time,  /,  may  be  determined  as  follows : 

The  original  volume  of  the  charge  is,  F=  n  ^  i:  R^  \  or, 
assuming,  as  before,  that  the  velocity  of  combustion  is  unity, 
V=z  n  -^  TX  r^,  the  unburned  volume  at  the  end  of  the  time, 

t,v7'i\\hev,-n^7T{r—ty=,v{l—[\   -      Therefore,    the 
volume  burned  will  be,  z/'=  V—Vf^z  V\  1 —  (  1 —  -  j  (4) 

Similarly  w'  =  ^F  1—  (  1—  ^)'  1  -        (5) 

The  curve  whose  ordinates  express  the  relation  w'  z=.  f  {t) 
will  be  of  the  form  shown  in  figure  7,  and  figure  1,  chap.  XII. 


XI. — COMBUSTION    IN    A    GUN 


CHAPTER  XI. 
COMBUSTION  IN  A  GUN. 

PRESSURES. 

Comparison  to  Steam. 

For  purposes  of  illustration,  the  action  of  gunpowder, 
when  burning  in  a  gun,  may  be  compared  to  that  of  steam 
in  the  cylinder  of  a  steam  engine;  and  the  pressures,/,  at 
different  lengths  of  travel,  x,  of  the  projectile  in  the  bore, 
may  be  represented  by  the  ordinates  of  a  curve  which 
expresses  the  relation  jf=f  [x),  in  the  manner  used  in  the 
indicator  diagram  of  the  steam  engine. 

The  operation  may  be  conveniently  analyzed  by  dividing 
the  volume  of  the  bore  into  two  portions,  viz.: 

1st.  That  through  which  the  elastic  gases  are  being 
evolved  from  the  burning  powder,  called  the  combustion 
volume. 

2d.  That  through  which  these  gases  are  expanding  under 
the  elastic  potential  acquired  during  combustion.  This  may 
be  called  the  expansion  volume. 

Thus,  the  circumstances  during  the  passage  of  the  pro- 
jectile through  the  combustion  volume  correspond  to  the 
admission  of  steam  to  the  cylinder  of  a  steam  engine,  and 
the  completion  of  the  combustion  to  the  action  of  the  valve 
which  cuts  off  the  supply  of  steam.  The  subsequent  expan- 
sion in  both  cases  is  limited  by  the  length  of  the  cylinder. 

This  important  difference  exists;  that  the  expansion, 
which  in  steam  is  treated  as  adiabatic  (without  loss 
of  heat  except  from  external  work),  and  which,  there- 
fore, leads  to  a  loss  of  temperature  due  to  the  work  done, 


XI. — COMBUSTION    IN    A    GUN. 


is,  in  the  gun,  supposed,  from  Noble  and  Abel's  experi- 
ments, to  be  isothermal^  and,  therefore,  under  Mariotte's 
law. 

DISCUSSION. 

Hypotheses. 

In  the  following  general  discussion  we  will,  for  simplicity, 
begin  by  assuming  that  the  projectile  starts  freely  from  its  seat. 
We  will  neglect  the  variable  volume  of  the  liquid  residue 
and  that  of  the  powder  remaining  unburned  at  any  time. 

We  will  also  assume  that  the  inflammation  is  instanta- 
neous.    See  Chap.  VIII. 
Notation. 

Taking  the  origin  of  co-ordinates  at  the  origin  of  motion; 
X  will  represent  either  the  path  of  the  projectile  or  the 
volume  described  by  the  translation  of  its  maximum  crosr 
section. 

The  volume  of  the  chamber,  ^,  or  the  initial  volume,  is 
composed  of  two  volumes,  viz.: 

c,  the  volume  actually  occupied  by  the  charge  of  powder 
including  its  interstitial  spaces. 

c\  any  excess  of  volume  besides  that  required  to  hold 
the   charge.     Therefore,   k=zc-\-c\    and,    for  the   reduced 

k 
length   of  chamber^  we  have  x,  -=l ^ ,  in   which   r  is   the 

radius  of  the  bore.     We  shall  first  take  c'  =  O. 

Let  w  represent  the  weight  of  a  charge  of  powder  which 
will  be  consumed  in  a  time  r,  and  let  w'  be  the  variable  weight 
of  w  converted  into  gas  at  the  end  of  any  time  /. 

Let  (S  represent  the  corresponding  sum  of  the  burning 
surfaces  as  in  Chap.  X,  and  '2  the  sum  of  the  initial  sur- 
faces. 

Let  /  represent  the  variable  intensity  of  the  gaseous 
pressure  per  unit  of  area  on  the  base  >f  the  projectile;  and 


XI.— COMBUJ^TION   m   A   GUN. 


assume  any  particular  value  o.  /  to  be  uniform  throughout 
the  volume  occupied  by  the  gases,  the  density  of  which  is  d. 

Let/  be  taken  in  such  units  that  R^  Chap. IX, be  equal  to 
unity. 

Let  W  represent  the  weight  of  the  projectile,  the  radius 
of  the  cross  section  of  which  is  r\  the  variable  velocity  of 
which,  in  the  bore  is  v\  and,  at  the  muzzle  of  the  gun  is  V. 

Let  q  and  Q  represent  the  quantities  of  work  done  upon 
the  projectile  to  give  it  the  velocities  v  and  V. 

FORM    OF    PRESSURE    CURVE. 

Upon  firing  the  charge  the  combustion  volume  is  gradu- 
ally filled  with  gas,  the  density  of  which  will  vary  directly 
with  w'  and  inversely  with  x-\-c\  so  that  we  may  write 

w' 

Differentiating  this  equation,  considering  /,  w*  and  x  as 
variables,  and  dividing  through  by  dx^  we  have 
dp  __ 


dx      x-\-c 


1     i  dw*         w*  \ 
'^c\dx        x^cX 


(2) 
(3) 


But,  since  q=f  p  dx^ 

dp  _  _1_^  /  dw'—dq  \ 
dx  ~  x-\-c  \         dx        J 
Or,  dividing  both    numerator  and   denominator   of   the 
expression  in  the  parenthesis  by  dt  and  remembering  that 
dw' 


dt 


Similarly, 


dp  _        1         /  dq  \ 

dx  '~  {x^c)vy        dt  )'  W 

dp 


No  simple  law  has  yet  been  discovered  connecting  (T,  x 
and  /,  and  these  equations  cannot,  therefore,  be  integrated; 


XT.— COMBUSTION  m   A   GUN. 


but,  remembering  that  (T  is  a  decreasing  function,  and  q 
an  increasing  function  of  /,  a  conception  may  be  had  of  the 
form  of  the  curve,  the  ordinates  of  which  express  the 
relation /=/  (^). 

The  inclination  to  the  axis  of  X  will  be  greatest  at  first 

when  6  is  large,  and  x  and  ~-  =p  v  are  small.     It  will  be 

Oy  or  /  will  be  constant,  when  the  gas  is  evolved  just  fast 
enough  to  compensate  for  the  increasing  volume.  From 
this  point  the  conversion  is  not  rapid  enough  to  keep  up 
the  maximum  pressure,  so  that  the  pressure  will  fall  off 
until  a=.Oy  as  at  «,  Fig.  1,  from  which  point  the  curve  will 
be  an  hyperbola  with  the  axis  of  X  as  an  asymptote,  since 
p  becomes  equal  to  a  constant,  w,  divided  by  x-\-c.  By 
the  law  of  continuity,  a  should  be  a  point  of  inflexion  and  a 
point  of  tangency  between  the  combuscicn  and  the  expan- 
sion curves.* 

The  same  results  will  follow  when  /  is  taken  =/'  {t),  ex- 
cept that  the  inclination  of  the  tangent  to  the  curve  will 
vary  more  gradually. 

I.    PRESSURES    DURING    COMBUSTION. 

Effect  of  Size  of  Grain. 

Although  we  do  not  know  the  law  which,  in  the  gun,  con- 
nects (T=/(/)  and  x  =  Qf  (/);  experiments  with  Noble's  and 
Ricq's  apparatus  demonstrate  that,  when  nearly  equal  charges 
of  powder,  a  and  b,  in  which  H^  >  Z^^  are  fired ;  for  small 


♦The  parenthetical  expression  refers  to  the  relation  between  the  poten- 
tial energy  of  the  unburned  powder  and  the  kinetic  energy  of  the  projec- 
tile ;  for  n,  the  potential  energy  of  the  charge  must  always  be  equal  to 
7r  =  /(CT),  that  residing  in  the  unburned  charge;  -]-  q=f^  (v),  the  work 
already  done  at  any  instant;  -\-e=/^^  (/),  the  work  which  the  elastic 
potential  of  the  gases  is  capable  of  doing;  or  H  =7r  -j-q-\-e. 


XI. — COMBUSTION   IN   A   GUN. 


values  of  x  and  /,  cp  (/)  changes  but  slowly  for  considerable 
variations  in/"  (/). 

The  small  change  in  the  form  of  cp  (t)  for  a  given  change 
in  the  form  of  /  (/)  is  probably  due,  on  one  hand,  to  the 
relative  constancy  of  the  initial  resistances  to  motion,  or 
the  molecular  work  (Michie,  Art.  25),  and  on  the  other  hand, 
to  the  great  changes  in  /  {t)  resulting  from  the  cumulative  in- 
fluence upon  the  velocity  of  combustion  of  high  pressures 
when  (7  is  large.     Chapters  VIII.,  X. 

If,  therefore,  during  the  critical  period  of  combustion,  we 
assume  that  qp  (/)  is  nearly  constant  for  all  sizes  of  grain; 
V,  and  therefore  ^,  may  be  taken  as  independent  of  o.  Con- 
sequently, Eq.  4  shows  that  during  combustion,  the  inclina- 
tion of  pressure  curves  corresponding  to  different  values  of 
Z  will  be  an  increasing  function  of  a ;  or  for  equal  charges, 
the  smaller  the  grain,  the  steeper  the  curve.  Similar  reason- 
ing shows  that  it  will  also  be  higher. 

Experiine7ital  Illustration. 
This  may  be  re'presented  by  fig.  2,  derived  from  Noble's 
experiments,  in  which  a  represents,  by  its  ordinates,  the  suc- 
cessive surfaces  of  a  charge  of  fine-grained  powder  burned 
in  the  air,  its  initial  portion  only  being  represented.  The 
curve  a'  shows  the  effect  produced  upon  its  burning  by  con- 
finement in  the  gun.  Let  b  and  b'  similarly  represent  the 
varying  surfaces  of  an  equal  charge  of  coarse-grained 
powder.  Let  a  and  /3  be  corresponding  curves  representing, 
by  their  ordinates,  the  velocities  acquired  by  the  projectile  at 
any    time,  /.     For    any   time  /,  the  area  under   a'   or  b'  = 

J  a  dt=w' ;  and  similarly  the  area  under  a  ox  (i=J  vdt—.x-^c. 

Under  the  circumstances  named,  although  Z^=*^  Zy,,  the 
curves  a.  and  |3  were  nearly  coincident  in  their  initial  por- 
tions. These,  which  we  shall  term  the  v  curves  and  the  a 
curves,  have  the  axis  of  time  m  common. 


XI. — COMBUSTION   IN   A   GUN. 


At  any  time  /,  which  is  less  than  tb,  the  time  required  for 
the  combustion  of  the  powder  ^,  the  ratio, =/»  is  less 

for  the  coarse  grained  powder  than  for  the  fine.  At  t^  ^^d 
Tb  expansion  begins ;  at  r^  the  pressures  from  the  two  pow- 
ders will  be  nearly  equal  to  each  other,  since  the  same  weight 
of  powder  in  each  case  is  burned  in  nearly  equal  volumes. 

Similar  effects  would  follow  the  changes  in  a,  indicated  in 
Chap.  X.,  from  whatever  cause  the  rate  of  change  of  o  was 
varied. 

The  best  results  would  be  attained  when  both  the  <j  and 
V  curves  coincided  in  such  a  line  as  ^,  fig.  2,  since  we 
would  then  have  the  constant  pressure  sought  for  in  the 
ideal  gun. 

The  effect  upon  pressures  of  varying  the  size  of  grain,  or 
the  rate  of  burning  in  charges  of  equal  weight,  would  be 
represented  by  the  curves  a,  b^  k,  in  fig.  3,  in  which  the  nota- 
tion of  fig.  2  is  preserved. 

Additional  Illustration, 

The  principle  is  illustrated  in  figure  10,  in  which  curves  a 
and  b  (which  to  avoid  confusing  the  drawing  are  omitted),  may 
be  imagined  to  result  from  Equation  (5),  Chapter  X,  and  a' 
and  b'  to  be  constructed  from  a  and  b^  in  the  manner  indi- 
cated in  figure  2.  The  curves  a  and  ^  express  the  relation 
x=f'  (/)  as  in  figure  2  they  expressed  v=.f{t). 

The  ordinate  t  y'  represents  the  proportionate  part  w',  of 
the  original  weight  of  the  charge,  w^  (represented  by  O  7v), 
that  has  been  burned  in  the  time  O  t\  and  /  z'  the  volume,  x, 
through  which  the  projectile  has  moved  in  the  same  time. 
Similarly  for  the  curves  b'  and  /?. 

The  line  ^^  is  parallel  to  O  T^  and  at  a  distance  from  it,  on 
the  scale  of  the  axis  JT,  that  is  proportional  to  the  volume  of  the 

chamber..  Then^p-p-^  =  -^  =  ^=A.-  and  similarly 
for  the  curves  b'  and  ^. 


X!. — COMBUSTION   IN   A   GUN. 


In  figure  2  it  is  not  possible  to  represent  the  constant  of 
integration,  c, 

2.    PRESSURES    DURING    EXPANSION. 

The  locus  of  the  pressures  at  the  end  of  the  several  com- 
bustion periods  is  the  hyperbola  H,  fig.  3,  the  intersection  of 
which,  with  the  axis  of  P^  is  at  a  height  (9/,  corresponding 
to  43  tons  per  square  inch,  and  the  parameter  of  which  de- 
pends upon  the  weight  of  the  charge.  Thus,  the  hyperbola 
H'  would  be  the  locus  for  a  charge  greater  than  w,  and  its 
vertical  asymptote  would  be  at  a  distance  from  6?=  —Xi—c 
See  figure  5. 

Remarks. 

1.  The  relative  constancy  of  the  v  curves,  in  spite  of  con- 
siderable variations  in  /,  may  be  explained  by  considering 
the  gunpowder  as  a  reservoir  of  potential  energy.     In  this 

— ^ —  J ,  SO  that  v=J\^w')y  while  we 

have  seen  that/=/^^(w'). 

2.  It  is  probable  that  the  work  done  during  combustion 
is  proportional  to  the  weight  of  the  charge. 

ADAPTATION  OF  POWDER  TO  GUNS. 

The  preceding  discussion  shows  that  if  the  size  of  the 
grain  remains  constant,  the  pressure  increases  with  the  size 
of  the  charge. 

In  order  to  compensate  for  this,  General  Rodman  pro- 
posed to  increase  the  size  of  the  grain  as  the  caliber  of  can- 
non of  the  same  class  increased. 

This  is  the  basis  of  the  modern  practice  requiring  special 
powders  for  special  guns. 


XI. — COMBUSTION   IN    A    GUN. 


PASSIVE  RESISTANCES. 

Returning  to  fig.  1,  we  see  that  the  area  limited  by  the 
pressure  curve,  the  axis  of  X,  and  the  muzzle  ordinate  at  w, 
will  represent  the  work  done  by  the  powder  under  the  cir- 
cumstances named. 

The  greater  portion  of  this  work  appears  in  the  kinetic 
energy  of  translation  of  the  projectile;  and,  for  simplicity  in 
the  following  discussions,  all  the  work  will  be  considered  to 
have  been  so  transformed. 

The  difference  between  the  work  of  the  pressures  and  the 
energy  of  translation,  which,  in  practice,  may  amount  to 
about  ten  per  cent,  of  the  former,  is  due  to  the  work  of  the 
passive  resistances ^  including  the  waste. 

Eesistances. 

The  work  of  these  resistances  is  equal  to  the  sum  of  the 
following  quantities  of  work: 

1.  That  done  in  giving  rotation  to  the  projectiles  in  rifled 
guns  and  in  causing  recoil. 

2.  That  done  in  permanently  deforming  the  projectile  and 
the  gun.  The  former  is  practically  confined  to  rifled  pro- 
jectiles and  is  greatest  in  breech  loaders. 

3.  That  done  in  overcoming  the  friction  of  the  projectile, 
and  in  distributing  the  charge  in  the  form  of  gas  through- 
out the  bore. 

Waste. 

4.  The  waste  is  due  to  the  absorption  of  heat  by  the  walls 
of  the  gun,  and  to  the  escape  of  the  gases  past  the  projectile 
and  through  the  vent. 

Graphical  Representation. 

So  that  if  we  take  a  pressure  curve,  as  in  fig.  4,  and  draw  a 
line  R  R\  so  that  the  area  under  it,  corresponding  to  any 
length  of  path  x,  shall  represent  the  work  of  the  passive  re. 
sistances  during  the  motion  of  the  projectile  over  that  path, 


XI. — COMBUSTION   IN    A    GUN. 


the  segment  r/,  of  any  ordinate  x  p,  will  represent  that  por- 
tion of  the  total  pressure  which  gives  acceleration  to  the 
projectile  and  imparts  to  it  kinetic  energy  proportional  to 
the  area  included  between  the  two  curves  and  any  limiting 
ordinate. 

Remarks. 
Band. 

In  breech-loading  guns  the  initial  resistance  is  consider- 
able until  the  rotating  band  has  entered  the  rifling;  there- 
after the  resistance  diminishes  rapidly. 

Example:  In  a  9.5  in.  B.  L.  R.  a  charge  of  over  4  pounds 
of  powder  failed  to  move  the  projectile;  but  a  slight  increase 
in  the  charge  gave  it  considerable  velocity. 
"Waste. 

The  loss  of  energy  from  absorption  of  heat  by  the  gun 
increases  with  the  slowness  of  the  powder;  since  with  slow 
powder  the  velocity  of  the  projectile  is  less  at  the  moment 
of  maximum  temperature  or  pressure. 

It  varies  inversely  with  the  calibre,  since  with  charges  of 
the  same  proportions  the  weight  of  the  charge  varies  with 
r*,  while  the  surface  varies  nearly  with  r^. 

The  escape  through  the  vent  probably  increases  with  the 
slowness  of  the  powder. 

Instantaneous  Pressure. 
Variability. 

From  the  discussion,  Chap.  VII.,  it  is  evident  that  the  pres- 
sure at  any  instant  throughout  the  volume  in  rear  of  the  pro- 
jectile is  not  uniform,  but  increases  toward  the  bottom  of  the 
bore,  as  represented  by  the  variable  line/o/-     Fig.  4. 

Neglecting  the  passive  resistances,  the  intensity  of  the 
variable  pressure  at  the  bottom  of  the  bore,  generally  known 
as/o>  can,  by  analysis,  be  shown  to  be  very  nearly  equal  to 


/ 


(w  \ 


10 


XI COMBUSTION    IN    A    GUN. 


Considering  the  passive  resistance/o  is  taken  =//  1  +  yTvi- 

Supposition. 

For  an  elementary  discussion,  like  the  following,  such 

differences  in  the  instantaneous  pressure,  and  the  effect  of 

the  passive  resistances,  once  understood,  maybe  neglected. 

So  that  the  pressure  at  any  instant  upon  the  bottom  of  the 

bore  will  be  assumed  to  be  that  exerted  at  the  same  instant 

on  the  base  of  the  projectile,  and  all  of  it  is  supposed  to  be 

utilized  in  giving  motion  to  the  projectile. 

JV 
The  difference,  p  n  r' a,  evidently  tends  to  compress 

.     .  .  ^ 

the  projectile  in  the  direction  of  motion,  and  its  effect  will  be 

most  felt  at  the  base  of  the  column  of  metal  moved. 

Except  in  the  next  discussion,  in  which  actual  free  vol- 
umes are  considered,  the  origin  of  co-ordinates  is  always 
taken  at  the  origin  of  motion;  viz.,  at  that  section  of  the 
bore  occupied  by  the  base  of  the  projectile  when  the  gun  is 
fired. 

WORK  OF  FIRED  GUNPOWDER. 

It  is  not  necessary  in  practice  to  separate  the  work  of 
combustion  from  that  of  expansion;  but  the  total  work  which 
may  be  expected  from  a  given  charge  of  powder  may  be 
determined  in  the  following  manner. 
Total  Potential  Work. 

In  fig.  3  the  area  included  between  the  ordinate  O  P^  the 
axis  of  X,  and  the  hyperbola  H  at  infinity,  will  represent 
the  total  amount  of  work  which  this  charge  could  perform. 
Calling  this  i2,  we  see,  from  Chapter  IX.,  that  expressing, 
as  is  usually  done,  work  in  foot-tons,  and  w  in  pounds, 

/2=486  w. 
Actual  Potential  Work. 

If,  instead  of  expanding  the  powder  gases  to  infinity,  we 
limit  the  useful  work  of  the  expansion  by  placing  the  muzzle 


XI. — COMBUSTION   IN   A    GUN.  H 


as  at  m^  we  shall  have  an  area  which  will  represent  the 
maximum  potential  work  under  the  conditions  existing  in 
the  gun. 

This,  which  in  practice  is  not  much  over  —  ,  we  will  call  Q. 

Effective  Work. 

Now,  if  we  fire  the  charge  w  in  a  gun,  we  shall  give  a 
certain  velocity  F  to  a  projectile  W.  Calling  the  amount 
of  kinetic  energy  so  realized  E^  we  have 


E=. 


2^x2240 
The  ratio,  -—  =  F,    is  called  the  factor  of  effect.     It  is 

used,  as  hereafter  explained,  in  anticipating  the  results  of 
certain  changes  in  the  piece  and  ammunition. 

Fig.  3,  shows  by  the  triangular  areas  above  the  curves, 
a,  ^,  k,  the  principal  reason  why  7^  <  1. 

F  is  further  diminished  by  the  passive  resistances. 

MEASURE    OF    Q. 

To  deduce  a  formula  for  the  potential  work  of  the 
powder  gases  when  expanded  in  a  gun  of  a  definite  length, 
or  the  equivalent  of  the  area  Q^  we  use  the  general  equation 

^—^dx.  (6) 

Substituting  the  ;i^alue  of  /,  from  Eq.  3,  Chap.  IX,  and 
for  brevity  replacing  0.0025571  by  «,  and  0.048  by  by  we 
have,  since  all  linear  dimensions  are  given  in  inches, 

G"  (inch-tons)  =  ^ 


na  d* 


12 


XI. — COMBUSTION    IN    A    GUN. 


(2"  (inch-tons)  ='^  '         '^^ 


Takinrj,  in  this  case,  the  origin  of  co-ordinates  at  tne 
bottom  of  the  bore,  integrating  between  x^,  and  x' ,  corre- 
sponding to    O'  O  and  O'  m^  fig.  1;  substituting  the  value 

of  a^  and  remembering  that  Q=  ■^—  ,  we  have, 

^'-23.9  ^3 

e= 75.04  tt/,  log  ~  .  (7) 

^,-33.9  -, 

Volumes  of  Expansion. 

The  subtractive  term  above,  appears  from  the  form  of  the 
equation  and  can  be  shown  to  be  the  reduced  length  of  the 
residue,*  or 

/>=33.9^;  (8) 


pand  x^/—x^—p:  —  =z  n  ^  number    of 

volumes  of  expansion,  an  important  characteristic  of  a  gun. 
It  is  convenient  to  remember  that  p=:  about  -j^  the  length 
of  the  cartridge,  if  its  diameter  =d  above. 

Equation  7  may,  therefore,  be  written  under  a  form  con- 
venient for  general  discussion. 

(2=75.04  w.  log«.  *  (9) 

The  calculus  shows  that  the  curve,  the  area  between 
which,  the  asymptote,  and  two  ordinates  is  proportional  to 
the  logarithm  of  the  extreme  abscissa,  is  an  hyperbola, 
which  is  the  result  reached,  page  4. 

*  For  the  smokeless  powder  referred  to  in  Chapter  III,  p  will  be  prac- 
tically =  0,  n  will  diminish,  and  so  will  /o  for  equal  values  of  w.  The 
effect,  as  hereafter  discussed  under  Air  spacing,  will  be  to  make  the  powder 
more  progressive ;  unless  the  powder  belongs  to  the  class  of  high  explo- 
sives and  its  explosion  is  of  a  high  order. 


XI. — COMBUSTION   m   A   GUN.  1^ 


Consequently  if,  as  in  fig.  5,  we  assume    axes  of  P  and 
iV",  we   may   construct  various  hyperbolas  depending  upon 
the  value  of  w^  such  that  the  areas  under   them   will    give^ 
the  corresponding  values  of  Q. 

VARIATIONS. 

1.  In  Weight  of  Charge. 

The  hyperbolas  intersecting  at  the  point  P,  Fig.  5,  and 
Equation  7,  show  the  effect  upon  x,;  x' \  x,,;  x";  p;  n; 
Q ;  and  /,  resulting  from  variations  in  w. 

Inspection  of  the  figure  shows  that  an  increase  of  7Cf  to 
7£/  =:  -f  7i>,  decreases  n  from  about  12  to  7,  or  about  ^ ', 
the  total  length  of  the  bore  x'  =z  x"  remaining  constant,  as  in 
a  muzzle  loader. 

Owing  to  the  effect  on  n  of  variations  in  w,  Q  will  not  in- 
crease in  direct  proportion  to  w.  But,  in  a  given  gun,  log 
n  diminishes  so  much  less  rapidly  than  w  increases,  that  we 
may  for  simplicity  assume  that  n  is  constant;  and,  taking  a 
constant  ratio  between  n  and  x,  we  may  replace  the  axis  of 
iV^by  that  of  X,  and  complete  the  figure  by  drawing  upon 
it  combustion  curves,  as  in  Fig.  6,  so  that  for  the  same  weight 
of  charge  the  areas  under  the  combustion  curves  are  equal, 
without  regard  to  the  size  of  grain.     See  Remark  2,  page  7. 

2.  In  Size  of  Grain. 

The  curves  a'  a" ,  refer  to  different  weights  of  the  same 
kind  of  fine  grained  powder,  which  are  supposed  to  be 
burned  through  at  about  the  same  point  of  the  bore.  Curve 
a",  refers  to  a  weight  w  of  coarse  grained  powder. 

Consideration  of  Fig.  6,  shows  how,  by  increasing  both 
the  weight  of  the  charge  and  its  inherent  progressiveness, 
we  may  obtain  a  pressure  curve,  the  work  area  under  which 
may  equal  and  even  exceed  that  due  to  the  fine  grained 
powder,  without  incurring  the  risk  attending  the  high  pressures 
to  which  it  gives  rise. 


14  XT.— COMBUSTION   IN   A   GUN. 

In  other  words,  we  approach  the  conditions  required  in 
the  ideal  gun,  by  effectively  diminishing  the  value  of  n. 

For,  comparing  curves  a"  and  b" ^  figure  6,  it  is  evident 
that  the  latter  is  the  more  progressive,  or  more  nearly  parallel 
to  the  axis  of  X,  and  that  this  results  from  expansion  begin- 
ning further  down  the  bore.  Neglecting  the  areas  under  the 
combustion  curves,  the  inclination  of  which  in  the  diagrams 
is  purposely  exaggerated,  the  effect  is  practically  the  same  as 
if  the  powder  had  been  instantaneously  burned  in  a  volume, 
c  -\-  c',  greater  than  c,  page  2,  by  the  volume  through  which 
the  projectile  had  moved  before  expansion  began.    We  would 

x' p 

then  have  n'  =: ,     ,    —  <  n.     See  Air  Spacing, 

x,  +  c'—p 

3.  In  Length  of  Bore. 

While,  in  all  cases  in  practice,  an  increase  of  O  m  increases 
Q  and  F,  the  proportionate  advantage  from  the  increase  of 
O  m  increases  with  the  progressiveness  of  the  powder. 

The  limit  of  useful  increase  of  O  mis  determined  by  the 
intersection  of  the  line  of  pressures  with  that  of  resistances. 
Fig.  4.* 

In  many  works  on  Gunnery  the  importance  of  Om^  or  the 
path  traversed  by  the  base  of  the  projectile  in  the  bore  of 
the  gun,  is  overlooked;  or  it  is  left  to  be  inferred  from  the 
total  length  of  the  bore. 

In  the  more  recent  and  advanced  works  it  has  a  specific 
symbol  u  by  which  it  will  be  hereafter  recognized. 

AIR  SPACING. 
Variations  in  A. 

We  have  so  far  assumed  the  powder  to  be  fired  in  its  own 
volume.  If  we  assign  to  the  charge  a  volume  greater  than 
that  required  to  contain  it  by  the  volume  ^',  page   2,  the 


*This  applies  to  small  arms.  For  heavy  cannon  the  increased  weight 
of  piece  resulting  from  the  prolongation  of  the  bore,  can  generally  be 
used  to  better  advantage  elsewhere. 


XI. — COMBUSTION   IN   A    GUN.  15 

value  of  A  will  diminish.  Eq.  8,  Chap.  IX.,  shows  that  the 
initial  pressure  will  also  diminish,  and  so,  under  given  con- 
ditions will  Q.     In  such  a  case,  Eq.  1,  will  take  the  form 

/= j — ,    and    the     curve     expressing    the    relation 

x-\-c-t-  c' 

p  =/  {x)  will  be  such  as  shown  in  fig.  7. 

Curve  1  expresses,  by  its  ordinates,  the  varying  pressure 
when  A  is  large,  and  curve  2  the  same  function  when  A  is 
small,  the  weight  of  the  charge  being  the  same  in  both  cases.t 

It  will  be  observed  that  the  effect  of  air  spacing  is  princi- 
pally felt  when  c^  is  large,  compared  with  x^  that  is,  when  cs 
and/  are  relatively  large. 

Also,  since  by  differentiating  Eq.  1,  regarding  w'  as  a 

df)  11) 

constant  and  x  +  k=-\^  we  have  -^  = r-^^;  the  inclination 

aA.  Ar 

of  curve  2,  will  be  less  than  that  of  curve  1.     The  values  of 

Q  and  B  will  therefore  both  be  smaller  for  curve  2. 

Increase  of  Charge. 

If  u  is  fixed,  this  effect  is  compensated  for,  as  before,  by 
increasing  w.  This  produces  the  effect  shown  in  the  dotted 
curve,  3,  fig.  7. 

APPLieATIONS. 

Air  spacing  is  principally  applied  to  muzzle-loading  can- 
non on  account  of  the  necessary  limit  to  their  length  imposed 
by  the  requirements  of  loading.  It  results  spontaneously  from 

t  To  familiarize  himself  with  the  principles  involved,  it  is  recommended 
that  the  student  construct  curves  1,  2,  3,  as  follows  : 

1.  Assume  a  maximum  pressure  of  say  24  units  and<:=l;  c^  =  o', 
10=1;  thenfor  jr  =  l,/  =  12;  for  x=2, /  =  - =8,  and  so  on. 

2.  Take  c^  =1.-,  /&  =  2;  w=:l,  as  above;  then  for  x  =  o,p^=12i 
for  x  =  2fp  =  Q,  and  so  on. 

3.  Take^=l  and  w  =  1.5;  then  for  x  =  o, p=-=18',  forjr=l, 
/  =  12,  as  in  No.  1;  forx  =  2, /=9  (greater  than  No.  1).  No.  3  will 
continue  above  No.  1  to  oo.  The  powder  is  more  progressive,  and  n  is 
decreased. 


16  XI. — COMBUSTION    IN    A    GUN. 

the  ease  with  which  their  projectiles,  particularly  those 
which  are  spherical,  take  up  their  initial  motion.  It  was 
probably  to  diminish  this  that  the  sal^of,  a  cylindrical  block 
fastened  to  the  rear  of  spherical  projectiles,  was  formerly 
employed,  although  other  reasons  are  generally  assigned  for 
its  use. 

Until  about  1880,  when  the  EngUsh  government  began 
to  adopt  exclusively  the  breech-loading  principle  for  heavy 
cannon,  air  spacing  was  largely  employed  for  s/wrf,  thick 
muzzle-\oa,dmg  cannon,  firing  large  charges  of  ^uick-huYn- 
ing  powder.  It  was  secured  by  making  the  diameter  of  the 
chamber  greater  than  that  of  the  bore.  This  was  objec- 
tionable in  sponging  and  it  weakened  the  gun. 

It  was  made  constant  by  providing  the  projectile  with 
stops,  which  held  it  at  an  invariable  distance  from  the  bottom 
of  the  bore.  But  this,  although  beneficial  in  preventing  the 
great  variations  in  pressure  and  velocity  which,  from  care- 
less loading,  are  apt  to  occur  in  ordinary  muzzle-loading 
guns,  increases  the  length  of  the  gun  in  the  region  of  its 
greatest  diameter. 

It  is  still  employed  to  some  extent  in  breech-loaders,  but 
is  yielding  in  importance  to  the  means  now  employed  for 
regulating  the  combustion  of  gunpowder. 

EFFECT  OF  THE  ROTATING  DEVICE. 

If  the  initial  motion  of  the  projectile  be  restrained  by  the 
compression  of  the  rotating  device,/  will  have  an  initial 
value  at  least  equal  to  the  resistance  offered  to  deformation, 
and,  since  the  powder  is  burned  under  higher  and  more 
constant  pressures,  n  will  be  greater  and  more  constant 
than  when  the  projectile  is  free  to  move. 

ADVAIsTAGtS    OF    BREEuH-LOADING    GUNS. 

General  Advantages. 

1.  The  simplicity  and  exactness  of  the  method  by  which 
the  value  of  n  may  be  regulated. 


XI. — COMBUSTION   IN   A   GUN.  17 

2.  The  ease  with  which  u  may  be  increased  without  inter- 
fering with  the  operations  of  loading. 

3.  As  will  be  hereafter  shown,  the  compressible  pro- 
jectiles used  in  breech-loaders  are  more  accurate  than  the 
loosely  fitting  projectiles  employed  in  muzzle-loading  guns. 

In  spite  of  the  greater  simplicity  of  construction  and  of 
operation  of  muzzle  loaders,  these  advantages  have  com- 
pelled the  adoption  of  breech-loading  cannon. 

Tactical  Advantages. 

The  tactical  advantages  of  breech-loaders  are  also  greater. 
Among  these  are — 

1.  Greater  facility  in  securing  cover  for  the  piece  behind 
defenses,  and  for  the  gunners  behind  the  piece. 

2.  Less  danger  and  difficulty  in  loading,  since  but  one 
charge  can  be  inserted  at  a  time,  and  the  operation  of  spong- 
ing is  less  important  than  with  muzzle  loaders. 

3.  Greater  facility  in  examining  and  caring  for  the  bore. 

4.  Greater  facility  in  adjusting  the  charge  or  fuze  after 
loading. 

5.  ImmovabiUty  of  the  projectile  in  marching.  This  per- 
mits batteries  to  come  into  action  rapidly,  when  under  fire. 

6.  The  rapidity  of  fire  is  increased  for  large  pieces. 

The  price  paid  for  these  advantages  is  the  difficulty  of 
getting  officers  and  men  capable  of  working  the  cannon  with 
sufficient  care. 

OBJECTIONS    TO     INCREASING    WEIGHT    OF 
POWDER. 

The  preceding  discussions  show  that  we  compensate  for 
small  values  of  7i  by  corresponding  increases  in  the  value  of  w. 

The  objections  to  this  are  as  follows. 

1.  We  increase  the  waste  of  powder,  as  the  steam  en- 
gineer does  that  of  his  coal  by  failing  to  work  his  steam  ex- 
pansively. This  may  be  of  importance  when  storage  capacity 
is  limited,  as  on  ships  and  in  the  field,  and  it  tends  to  dimin- 
ish the  value  of  ?y,  hereafter  explained. 


18  XI. — COMBUSTION    IN    A    GUN. 

2.  The  work  done  in  distributing  the  gas  throughout  the 
bore  increases  with  the  weight  of  the  charge  and  the  length  of 
u.     Some  charges  now  weigh  half  as  much  as  the  projectile. 

3.  We  increase  the  tension  of  the  gases  within  the  gun  at 
the  instant  of  the  departure  of  the  projectile.  This  tends 
to  accelerate  the  recoil  and  to  perturb  the  flight  of  the  pro- 
jectile ;  since,  owing  to  their  small  mass,  the  gases  leave  the 
gun  with  a  higher  velocity  than  that  of  the  projectile. 

4.  Considering  the  gun  to  consist  of  a  number  of  staves, 
like  those  of  a  barrel,  the  moment  of  the  pressures  about  the 
breach  is  increased  on  account  of  their  greater  level  arm. 

5.  Variations  in  /  and  «,  due  to  accidental  variations  in 
the  velocity  of  combustion,  may  endanger  the  safety  of  the 
piece  or  affect  its  accuracy. 

IGNITION  AND  INFLAMMATION  IN  GUNS. 

The  importance  of  these  phenomena  has  largely  decreased 
with  the  adoption  of  the  breech-loading  principle. 

When  muzzle-loading  cannon,  firing  free  projectiles  with 

charges  of  fine  grained  angular  powder  were  generally  used, 

.1  . .       time  of  inflammation  , 

the  ratio -— ^ , —  was  large. 

total  time  of  conversion 

To  reduce  this  as  much  as  possible,  so  as  to  increase  the 
value  of  n^  the  charge  was  ignited  near  its  middle.  It  was 
found  that  ignition  in  rear  tended  to  waste  energy  by  moving 
the  forward  portions  of  the  unburned  charge ;  while  that  in 
front  reduced  the  velocity  by  the  premature  movement  of  the 
projectile. 

With  breech-loaders  the  charge  is  always  inflamed  before 
the  projectile  has  moved. 

The  shape  and  size  of  the  grain  and  the  use  of  a  special 
priming  of  quick  powder  placed  near  the  vent,  reduce  the  value 
of  the  ratio  of  times  above  referred  to  so  much,  that  the 
position  of  the  vent  is  determined  by  other  considerations. 


XI. — COMBUSTION   IN   A   GUN.  19 

MEASURES  DEPENDING  UPON  THE  MUZZLE 
ENERGY  OF  THE  PROJECTILE. 

1.    MILDNESS    OR    PROGRESSIVENESS. 

P  =:  /  TT  r^  is  called  the  variable  total  pressure. 

In  this,  and  in  subsequent  similar  expressions,  r  is  expressed 
in  the  same  linear  units  as  those  of  the  area  upon  which  /  is 
estimated. 

When/  has  its  maximum  value,  as  indicated  by  the  pres- 
sure gauge,  and  taken  =  /„ ;  the  maximum  total  pressure  is 
P'  =  x'  p',  Fig.  8. 

The  area  under  the  pressure  curve  divided  by  u  gives  the 

mean  total  pressure  P,-=^  —  =  m  p,. 

u 

The  effective  length  ox  u'  =  —  =  O  x". 

Therefore,  if  we  represent  the  following  ratio  by  ju,  we 
have,  since  E  =  P'  u'  =  P,  u, 

^  =  ^^'!L^^^    ^^'  .  (10) 

^       P'       u        P' u       ^gp.-ar'u 
in  which /^  and  JVare  expressed  in  the  same  units,  and  g,  u 
and  Fin  the  same  units. 

This  coefficient  /x,  which  measures  the  ratio  of  the  area 
under  the  curve  to  that  of  the  circumscribed  rectangle,  may 
be  taken  as  the  measure  of  the  mildness  or  progressiveness 
of  the  action  of  the  gunpowder  under  the  circumstances  of 
any  particular  case. 

The  limit  of  the  ratio  for  all  ordinary  powders  is  evidently 
unity,  and  would  be  reached  only  in  the  ideal  gun. 

2.    ECONOMY. 

-p 
7)  =  —  is  a  valuable  datum  for  comparing  the  economy   or 

w 

efficiency  of  various  powders. 


^0  XI. — COMBUSTION    IN    A    GtjM. 

It  appears  from  figure  3  that  the  greater  is  the  efficiency, 
the  greater  is  the  maximum  pressure ;  or  that  the  violence  of 
gunpowder  increases  with  rj.  Also  from  figure  2,  that  the 
smaller  the  value  of  r,  or  the  quicker  is  the  gunpowder  in  a 
given  gun,  the  larger  will  be  the  value  of  t]. 

It  would  be  more  consistent  to  follow  the  method  adopted 
for  jLt,  the  value  of  which  is  independent  of  any  particular 
metrical  system  \  but  in  order  to  avoid  dealing  with  large 
numbers,  and  because  of  the  general  use  of  the  term  "  foot- 
tons  of  energy  per  pound  of  powder,"  we  shall  write 

3.    GENERAL    COEFFICIENT. 

The  preceding  discussions  show  that  all  expedients  intended 
to  increase  the  progressiveness  of  powder  decrease  the  muzzle 
energy  resulting  from  the  conversion  of  a  given  weight  of  the 
explosive  ;  or  decrease  rj. 

Thus,  when,  as  in  figure  3,  we  increase  the  size  of  the  grain, 
or  vary  its  form,  composition  or  density  so  as  to  increase  r ; 
or  when,  as  in  figure  7,  we  diminish  /^  by  decreasing  A,  we 
decrease  the  Factor  of  Effect ;  and  therefore,  in  order  to  ob- 
tain the  muzzle  energy  required,  we  must  increase  the  weight 
of  the  charge,  as  shown  in  figure  6. 

In  order  to  compare  the  performance  of  different  powders 
fired  under  the  same  conditions,  or  of  the  same  powder  fired 
under  different  conditions,  it  is  proposed  to  use  a  general  co- 
efficienty  known  as  x  '•  which,  since  fi  and  r]  are  both  desir- 
able, will  be  proportional  to  their  product ;  and  which,  since 
they  tend  to  vary  inversely  with  each  other,  will  have  an 
approximately  constant  value. 

This  relation  may  be  expressed  by  writing 

X-iin=  ^^mp.TTiP  uw'  ('^^ 


XI. — Oo^rBusTloW  in  a  gun.  61 

It  will  be  hereafter  more  fully  discussed. 

4.    STRENGTH   OF   GUN   CONSTRUCTION. 

//  =    -j^ ,  in  which  IV'  is  the  weight  of  the  gun  (in  the 

same  units  in  which  IV,  the  weight  of  the  projectile,  is  expres- 
sed) measures  the  height  through  which  the  gun  would  have  to 
fall  in  vacuo  to  acquire  energy  equal  to  that  residing  in  the 
projectile  at  the  muzzle  of  the  piece. 

Thus  the  old  10  in.  S.  B.  C.  I.  gun  had  a  value  of  ^  =  300 
ft.  When  strengthened  by  a  rifled  steel  tube  that  reduces  its 
caliber  to  8  in.  we  have  the  "converted"  8  in.  Rifle,  for  which 
A  is  about  350  ft. 

For  the  new  8  in.  B.  L.  R.  Sfee/,  h  is  nearly  500  ft. 

6.    FACTOR    OF    EFFECT. 

The  meaning  and  derivation  of  this  have  already  been 
explained. 
Use. 

It  is  used  for  anticipating  the  effect  of  changes  in  the 
interior  form  of  a  piece,  or  in  its  ammunition,  upon  the 
muzzle  energy  of  the  projectile. 

It  differs  from  the  use  of  x  ^"^  its  factors  in  taking  no 
heed  of  the  maximum  pressure  involved  in  the  result. 
Conditions. 

It  is  necessarily  assumed  to  remain  constant  during  the 
variations,  the  effect  of  which  is  sought;  and  consequently, 
the  conditions  under  which  it  is  employed  should  be  as 
nearly  alike  as  circumstances  will  allow. 

These  conditions  relate  to  the  type  of  gun,  of  powder, 
and  of  projectile  employed  • 

Owing  to  the  greater  constancy  of  A,  and  to  the  high 
initial  pressure  required  to  move  the  projectile  from  its 
seat,  it  is  better  adapted  for  use  with  breech-loading  than 
with  muzzle-loading  cannon. 


M.  L.  R. 

B.  L.  R. 

30 

60 

50          1 

65 

75 

^  80-85 

85 

22  XI. — COMBUSTION    IN    A    GUN. 

The  factor  of  effect  increases  with  the  size  of  the  gun,  as 
seen  by  the  following  table,  giving  its  approximate  value, 
in  certain  individual  cases.  So  much  depends  upon  the  kind 
of  powder  used  that  only  the  most  general  conclusion  can 
be  drawn: 

Factor  of  Effect  Per  Cent. 

Muskets, 
Mountain  Guns, 
Field  " 

Medium        " 
Heavy  " 

APPLICATIONS. 

1.  Variations  in  w  and  a  . 

1.  Suppose  it  be  desired  to  estimate  the  change  in  the 
muzzle  velocity  to  be  expected  in  a  given  gun  from  certain 
charges  in  a/  or  A. 

The  values  of  E  and  Q,  under  known  conditions,  have 
been  determined;  and  therefore, 

F=  -yr  is  known. 

Determining,  from  Eq.  (7),  Q'  under  the  new  conditions, 
we  have-£''=i^  Q'.  On  firing  we  should  find  approximately — 

V=JJEl^.  (13) 

2.  Untried  Gun. 

2.  Suppose  that  we  desire  to  estimate  the  muzzle  velocity 
of  a  given  projectile  to  be  fired  from  a  new  and  untried  gun, 
of  which  we  have  only  the  drawings. 

We  select  the  record  of  some  gun  of  as  nearly  the  same 
type  as  possible,  assume  F=F\  and  proceed  as  before. 

3.  Dimensions  of  Guns. 

3.  The  inverse  problem  may  also  arise;  viz.,  to  determine 
the  interior  dimensions  of  a  gun  of  any  required  power. 


XI. — COMBUSTION   IN    A    GUN.  23 


Eq.  (7)  may  be  placed  under  the  form — 

w 

Q=l!6Mwlog (l4) 

^,-23.9,-^ 

The  calibre  and  the  density  of  loading,  A,  are  always 
assumed,  the  former  depending  upon  the  service,  and  the 
latter  upon  the  strength  of  the  gup;  therefore,  since 

27.68  w 


A  = 


V=7C  —  X,, 

110.72 «;  (15) 


'  TT  ^2   A 

We  have,  therefore,  two  problems: 

1.  Assuming  u  to  find  the  necessary  values  of  w  and  x^, 

2.  Assuming  iv  to  find  u. 

The  difficulty  of  simplifying  an  expression  of  the  form 
of  Eq.  (14)  requires  these  solutions  to  be  made  by  trial. 
In  the  first  case,  taking  F  from  some  similar  gun,  we  have 

01  =■  —=r-    Then,  assuming  successive  values  of  w,  we  insert 

them  and  the  corresponding  values  of  x^,  determined  from 
Eq.  (15)  into  Eq.  (14)  until  a  suitable  value  of  Q^  is  obtained. 

In  the  second  case,  we  proceed  as  before,  substituting 
successive  values  of  u. 

The  initial  approximations  to  the  value  of  u  will  be  facili- 
tated by  reference  to  the  value  of  n,  usual  in  guns  of  the 
type  proposed. 

EXAMPLES   FOR   PRACTICE. 

1.  The  3.20  B.  L.  W.  I.  Chambered  Rifle,  in  which  x,^ 
12  in.;  u=  56.1  in.;  3  lbs.  I.  K.  powder  =  ze/,  gave  to  a  I'Z 
lb.  projectile,  F=  1548/.^. 


^4  XI. — COMBUSTION    IN    A    GUN. 


Determine  its  factor  of  effect; 

j,_   E  _  199.3  _ 

2.  Estimate  V  for  a  13  lb.  projectile  to  be  fired  from 
the  new  3.20  B.  L,  Steel  Chambered  Rifle  with  a  charge  of 
3.75  lbs.  I.  K.  powder. 

From  the  drawings  we  find  that  the  volume  of  the  cham- 
ber, which  is  a  truncated  ellipsoid  terminated  by  various 
cylindrical  and  conical  surfaces,  when  diminished  by  the 
volume  of  that  portion  of  the  projectile  which  lies  within  it, 
=  123.157  cubic  in.  Similarly,  the  length  of  the  rifled  por- 
tion of  the  bore,  when  increased  by  that  of  the  projectile 
lying  within  the  chamber,^  73.24  in.  Therefore,  ^^=  15.31 
in.,  x'  =  88.55  in;  and  in  the  case  supposed  n  =  about  12  as 
before. 

We  find  (2' =  303.9  ft.-tons,  ^=247.4  ft.-tons,  and 
F=1657/.J. 

By  experiment,  F=  1662  f.s. 

The  difference  falls  within  that  usually  found  when  all 
the  conditions  are  as  nearly  constant  as  possible. 

DISCUSSION  OF  THE  COEFFICIENT  X. 

A  study  of  many  records  shows  that  when  the  conditions 
of  loading  approach  those  sanctioned  by  experience,  the 
value  of  X  expressed  in  the  units  assumed  varies  from  about 
24.0,  when  the  powder  is  so  quick*  with  relation  to  the  gun  in 
which  it  is  to  be  used,  that  the  weight  of  the  powder  is  only 
about  one  quarter  the  weight  of  the  projectile  ;  to  about  35.0, 
when  the  powder  is  so  slow  that  7a  may  be  safely  increased 
to  about  one  half  the  weight  of  the  projectile. 

*  The  remark  on  page  6  shows  that  the  same  powder  may  be  quick  in 
some  guns  and  slow  in  others.  Thus  the  powder  suitable  for  a  field 
piece  would  be  too  slow  for  a  musket,  and  too  quick  for  a  siege  piece; 
and  in  two  siege  pieces  of  the  same  caliber,  this  powder  would  be  quicker 
in  a  gun,  than  in  a  howitzer  or  mortar. 


XI. — COMBUSTION    IN   A   GUN.  25 

It  is  rare  to  find  a  value  of  x  ^vith  any  form  of  black  pow- 
der greater  than  28.0;  while  with  cocoa  powder  it  often 
approaches  35.0.  Furthermore,  these  values  approach  con- 
stancy, as  will  be  seen  from  the  table  on  following  page. 

The  approximate  constancy  of  x  enables  conclusions  to  be 
drawn  from  otherwise  perplexing  data.  Thus,  in  the  7.0  in. 
Howitzer  in  Table  I.,  it  might  be  difficult  to  decide  which 
was  the  better  powder,  L.  X.  B.  or  I..  K.  K.;  but  the  values 
of  X  show  that  the  former  is  to  be  preferred. 

If  we  assume  axes  of  ?/  and  fj,  as  in  fig.  9,  we  may  refer  to 
them  as  asymptotes  certain  hyperbolas  which  will  limit  all 
reciprocal  values  of  rj  and  ^  for  each  kind  of  powder.  Thus 
powder  /^,  for  any  assigned  value  of  7]  or  fi  will  give  a  higher 
value  of  [J,  OT  rj  than  powder  a. 

0(  the  two  principal  ballistic  data,  viz.:  Fand  /„,  the 
former  is  much  more  easily  and  certainly  obtained  than  the 
latter.  Indeed,  unless  the  pressure  gauges  are  carefully  pre- 
pared by  experienced  observers,  their  indications  are  fre- 
quently mconsistent. 

Therefore,  a  known  value  of  x  ^'^^Y  be  employed  to  check 
the  records  of  the  pressure  gauges,  or  to  replace  them;  for, 
having  observed  V,  we  have 

^"     ;^  2240  ^^77^/^  7/  ^     ^ 

Also,  having  ascertained  by  experiment  the  value  of  \i^  or  of 
7\  for  any  powder  of  which  we  know  the  coefficient  x^  ^^^  may 
estimate  the  weight  of  the  charge  of  that  powder  required  to 
give  to  a  projectile  of  any  desired  weight  the  maximum 
velocity  which  the  limit  of  pressure  imposed  by  the  construc- 
tion of  the  piece  permits,  or 

The  density  of  loading  will  be  regulated  by  this  value  oi p^. 
As  will  be  shown  in  Chapter  XII.,  the  value  of  X-,  for  the 


26 


XI. — COMBUSTION    IN    A   OUN. 


Sphere  Hex'l  powder. 
Converted  gun. 
Steel  gun. 

Flat  powder. 

Black  Prism. 

Hexagonal. 

Reported  "good." 
Reported  "good." 
Rep.  "entirely  too  quick" 
Rep.  "entirely  too  slow." 

^ 

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5r 

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oooi-ioooitooiCiTt^inTfmt^co'oicot^TtiQO 

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lOCOCOCOCOCOfMiflTtitDOiOSOSCOTfOOOr-l 

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M  w  w  w  w  ><  ^  'i  ^  ><  ><  ^  wV  >^  izi  ^'  <i  p=3 

vj  k4  fj  KH*  w  h4  c»  S  6  J  J  J  J  h  k  cu  d>Q^  d» 

S 

3 

urj  in  u'.  o  o  CO  o  lo  »o  o 

COOOCOCOCOCO-^TtiTtiOOOOrM(M''<!lHTj<-<:j3TlJ 
(M  ^  (M  (M  (M  (M  ^  (M  (M  -<  —  r-H  r^  —  -*(?}  (M  -M  (M 

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coeococococoidu^int-^r^iT-t^ooQOGdGOOOGO 

^ 

3 

XI. — COMBUSTION   IN   A   GUN.  27 

same  powder  fired  in  the  same  gun,  will  increase  as  the  ratio 
—  mcreases ;  but  a  nearly  constant  expression  called  11  will 

result  from  multiplying  the  computed  value  oi  xhy  j  —  j  ^  or 

\  W  /         /„  a    u  wl 
log  6^=6:2161. 

By  comparing  different  values  of  IT,  we  may  compare  the 
performance  of  different  powders  in  the  same  gun,  even  when 
fired  with  different  charges,  provided  the  weight  of  the  pro- 
jectile is  constant,  which  is  usually  the  case.* 

THEORY  OF  COCOA  POWDER. 

The  facts  that,  although  almost  all  possible  combinations 
of  the  ingredients  of  ordinary  black  powder  have  at  different 
times  been  tried  without  decided  advantage  over  those  gen- 
erally adopted;  and  that,  as  we  have  seen,  the  changes  in 
manufacture  which  have  had  as  their  object  an  increase  in  \i 
have  necessarily  correspondingly  reduced  ?/,  indicate  that  the 
difference  in  the  action  on  the  brown  powder  is  due  to  some 
marked  difference  in  the  chemical  composition  of  its  charcoal. 

This  was  for  some  time  a  secret  for  which  it  is  said  that  the 
British  Government  paid  a  large  sum.  Without  requiring 
such  payment,  the  Messrs.  Du  Pont,  of  Wilmington,  Dela- 
ware, the  manufacturers  of  a  powder  that  has  shown  itself  to 
be  nearly  equal  to  that  made  abroad,  have  furnished  the  basis 
of  the  following  theory  as  to  its  peculiar  behavior. 


*  So  many  of  the  records  require  the  value  of  u  to  be  assumed  from  the 
proportions  of  the  gun,  and  so  doubtful  is  the  accuracy  of  many  of  the 
pressures  recorded  before  the  theory  of  the  pressure  gauge  was  well 
understood,  that  the  constancy  of  x  ^o""  ^  given  gun  and  powder  is  best 
seen  from  an  analytical  discussion  in  Chapter  XII.  The  table  is  given 
rather  for  illustration  tha\.  for  proqf. 


28  XI. — COMBUSTION   IN   A    GUN. 

The  charcoal  made  by  superheated  steam  contains  a  large 
proportion  of  free  hydrogen  and  much  more  in  relatively 
unstable  combination. 

The  carbo-hydrates^  as  are  termed  the  resin,  gum  and 
sugar  added  during  manufacture,  are  also  magazines  of 
hydrogen. 

The  effect  upon  the  velocity  of  combustion,  due  to  the 
presence  of  the  gum  and  to  the  high  density  of  the  powder, 
and  possibly  also  some  of  the  phenomena  of  dissociation 
under  high  pressures,  prevent  the  sudden  liberation  of  the 
hydrogen  and  its  combustion  when  x^  Eq.  (1),  is  small. 

The  hydrogen  combines  as  the  pressure  wanes,  and  tends 
to  sustain  the  pressure  and  to  increase  both  7\  and  //,  whereas 
in  black  powder  they  must  vary  inversely. 

The  water  formed  serves  to  precipitate  the  smoke,  the  solid 
particles  of  which  are  entangled  in  a  condensed  spray  of 
liquid  gum  following  the  projectile. 

To  this  may  be  added,  as  a  theory  more  generally  accepted, 
that  the  large  proportion  of  nitre  tends  to  prevent  the  forma- 
tion of  CO,  thus  reducing  the  volume  of  the  gases  first  formed, 
and  diminishing  the  violence  of  their  action,  or  increasing  \ji„ 
On  the  other  hand,  the  excess  of  nitre  may  tend  to  increase 
7\  on  account  of  the  more  perfect  combustion  of  the  charcoal 
and  the  high  calorific  value  of  the  hydrogen  which  it  contains. 

The  precautions  usual  in  manufacture  are  taken  to  affect  the 
size,  shape  and  density  of  the  grain  and  the  amount  of  moist- 
ure it  contains,  so  as  to  increase  its  progressiveness. 

That  these  precautions  alone  do  not  account  for  its  peculi- 
arities appears  from  the  fact,  that  while  a  prism  of  black 
powder  burns  in  the  open  air  in  \\  seconds,  and  a  similar 
prism  of  brown  powder  burns  in  10  seconds,  equal  charges 
of  the  brown  powder  give  equal  or  higher  muzzle  energies 
than  the  black  powder  without  exceeding  their  maximum 
pressures. 


XI. — COMBUSTION    IN   A   GUN.  29 

English  Experiments  of  1890. 

1'hese  furnish  the  following  data  from  which  the  effects  of 
the  composition  of  the  powder  may  be  observed. 
SoHd  residue  per  cent : 


Permanent  gases  per  cent  of  volume  : 


7\  oi  permanent  gases  above 
Heat  units  per  kilogramme 
/=  v^  H.    (Chap.  IX,  page  7)  ratio 
Specific  volumes  of  water  vapor 


Black. 

Brown. 

K.CO, 

m 

64 

Kir  CO, 

— 

14 

s 

9 

— 

K,S 

15 

— 

KSO, 

10 

22 

iim(3  • 

100 

100 

UIIlC  . 

CO, 

47 

51 

CO 

16 

3 

H,S 

3 

— 

ZTand  CH^ 

4 

4 

N 

30 

42 

100 

100 

278 

198 

721 

837 

•atio 

1.0 

0.83 

41 

122 

XII. — SARRAU  S  FORMULAE  FOR  INTERIOR  BALLISTICS. 


CHAPTER   XII. 

SARRAU'S  FORMULAE  FOR  INTERIOR 
BALLISTICS. 

The  deductions  of  M.  Emil  Sarrau  permit  a  very  accu- 
rate solution  of  many  important  problems  affecting  the 
interior  form  and  the  method  of  loading  cannon. 

By  methods  which  are  too  elaborate  for  present  instruc- 
tion, Sarrau  deduces  four  general  formulae  for  pressures 
and  velocities. 

Notation. 

The  units  in  the  following  notation  are  based  upon  those 
adopted  in  the  publications  of  the  Ordnance  Department, 
U.  S.  A.  Some  changes  are  made  in  the  notation  to  make 
it  agree  with  that  previously  used  in  this  work.  Where 
Sarrau's  notation  differs,  it  is  given  in  brackets. 

Let 
V.    (v)  Muzzle  velocity,  in  feet  per  second, 
/o  (F^  Maximum  pressure  on  bottom  of  bore  in  pounds 

per  square  inch. 
/    {P)  Same  on  base  of  projectile. 
d.  (c)     Caliber  in  inches. 
u.  Length  of  the  travel  of  the  base  of  the  projectile  in 

the  bore,  in  inches.     See  Chapter  XI,  page  13. 
W  (/)  Weight  of  projectile  in  pounds. 
w  {n)    Same  of  powder. 
A  Density  of  loading. 

d  Specific  gravity  of  the  powder. 

N'  The  granulation  of  the  powder,  or  the  number  of 

grains  per  pound. 


2       XII. — SARRAU'S  FORMULA  FOR  INTERIOR  BALLISTICS. 

/  Force  of  powder  when  A  =  1,  Chapter  II,  page  7. 

r  Time  of  combustion  of  a  single  grain,  referred  to  a 

standard  grain  as  unity.     See  page  5. 

S  Initial  volume  in  cubic  inches;  the  same  as  F,Chap- 

ter  IX,  foot  page  3.  This  volume  generally 
differs  from  the  capacity  of  the  powder  chamber 
since  the  base  of  the  projectile  may  occupy  some 
of  this  space. 

8  The  reduced  length  of  the  initial  air  space  which  is 

equal  to  v'  (Chapter  IX,  page  3)  +  ^'  (Chap- 
ter XI,  page  2). 

We  have  z=S — v.  but 

4  ' 

e      27.68  7£/       ,          27.68  7£/     ,,       . 
o.= and  z^,= :  therefore 


A 
110.72  w 


(i4) 


a  and  /  (Sarrau  uses  \  instead  of  /). 

These  are  two  numerical  coefficients  depending  on 
the  form  of  the  grain,  which  are  functions  of  the 
ratio  of  the  least  dimension  of  the  grain  to  its 
other  dimensions.     See  page  3. 

a  and  fi.  Two  very  important  characteristics  depending 
on  the  nature  of  the  powder;  viz,  both  on  its  form 
and  the  time  of  its  combustion.  Their  values  are 
obtained  from  the  following  equations  : 


m 


^=  r  (3) 

Owing  to  their  preponderating  effect  in  the  prin- 
cipal equations  which  follow,  a  is  known  as  the 


XII. — SARRAU'S  FORMULif:  FOR  INTERIOR  BALLISTICS.       3 

pressure  characteristic^  aod  p  as  the  velocity  char^ 
acteristic. 
A,  B,  M,  K.  Certain  empirical  constants  to  be  determined 

by  experiment. 
Form  of  Grain. 

If  we  develop  Equation  5,  Chapter  X,  according  to  the 

ascending  powers  of  —  the  development  may  be  placed 
under  the  general  form  * 

j=/w=<.i(i_/i+«i;+&c. . . . .)    (4) 

This  may  be  shown  to  apply  to  other  forms  of  grain 

besides  the  sphere,  the  coefficients  of  —  varying  with  the 

form  of  the  grain  and  by  their  values  characterizing  the 
mode  of  combustion  in  so  far  as  it  is  affected  by  the  form 
of  grain. 

I.  For  spherical  grains  it  readily  appears  that 
a;  =  3;        /=  1;         m  =  Yi, 
The  coefficient  m  is  neglected  as  insignificant. 

Besides  the  spherical  grain,  which  includes  not  only  true 
spheres,  but  grains  the  form  of  which  approaches  that  of  a 
sphere,  such  as  cubes,  hexagonal  powders  and  those  of 
irregular  granulation ;  powders  are  classified  as  to  form,  as 
parallelopipedons  and  pierced  cylinders.  Both  classes  in- 
clude the  forms  most  closely  resembling  the  type,  e.  g.  L.  X. 
powder  would  belong  to  the  former,  and  pierced  prismatic 
powder  to  the  second  class. 


*  In  the  above  equation  replace  —  by  jr,  then 
f  {t)  =z\—  {X  —  x)^  =^^  X  —  2,  x"  ■\-  x^ 

=  3-(i  —  +  -')  =  T  [1-7+1(7)'] 

For  grains  of  other  forms  a  similar  but  more  extended  method  is  followed. 


4        XII. — SARRAU'S  FORMULAE  FOR  INTERIOR  BALLISTICS. 

II.  For  the  parallelopipedon,  if  x  and  j^  represent  the  ratios 
of  the  least  dimension  of  the  grain  to  its  other  two  dimensions 

the  development  of  the  corresponding  function  of  —  will  give 

T 

the  following  characteristic  values  for  the  coefficients  a  and  /, 

a 
If  the  base  of  the  grain  be  square,  x  —  y^  and 

a=.\-\-%x;  I—  •• 

a 

III.  For  the  pierced  cylinder,  x  represents  the  ratio  of  the 
thickness  of  the  walls  of  the  cylinder  to  its  height,  or  con- 
versely; the  lesser  dimension  being  divided  by  the  greater 
in  either  case.  The  cylinder  is  supposed  to  burn  all  over 
at  once.  The  following  are  the  values  of  the  coefficients 
for  the  pierced  cylinder  described: 

a=:l-{-xj    1=  -. 
a 

Since  the  ratio  x  has  generally  given  to  it  a  value  of  J 
we  may  form  the  following  table. 


TABLE    I. 


Values  of  ^ 


Form  of  Grain.  a  I 

I.  Cubical;  Spherical;  Hexagonal; 

Irregular  granulation  3.0         1.0         3.0 

II.  Parallelopipedon ;  flat  powder  2.0  g  3.2 

III.  Pierced  prism  or  cylinder,  one  hole     f  J  4.5 

By  substituting  these  values  of  a  and  /  in  Eq.  (4)  we  may 

represent  graphically,  as  in  figure   1,  the  variations  in  the 

rate  —=^o  for  grains  of  equal  weight  but  of  different  forms, 
burning  in  the  same  time  t. 


XII. — SARRAU'S  FORMULAE  FOR  INTERIOR  BALLISTICS. 


If  the  rate  of  conversion   is   uniform,    Eq.  (4)  becomes 

t 
f  {t)-=.a-  and  /,  /?  and  y  (post)  reduce  to  0. 

T 

Size  of  Grain. 

The  mean  diameter  of  irregular  grains  results  from  know- 
ing their  specific  gravity  and  granulation  as  follows* 

/6x27.68\i       /  52.86  \1 

For  powders  of  regular  granulation  a  similar  method  may 
be  preferred  to  the  actual  measurement  of  their  dimensions. 

VELOCITY  FORMULA. 
Monomial  formula  for  quick  powders 


'=Ma  (i) 


Binomial  formula  for  slow  powders 


(A) 


in  which 


F=Aa(wu)^^-^y[l-rl  (B) 

The  choice  of  the  formula  to  be  employed  in  any  case 
depends  upon  the  value  of  y.  With  a  given  gun  and  pro- 
jectile this  depends  upon  the  value  of  /3  and  therefore, 
under  the  conditions  of  loading,  /3  measures  the  quickness 
of  the  powder. 

The  form  of  the  function  y  shows  that  its  value  depends 
largely  upon  the  gun  as  well  as  upon  the  powder.     Conse- 

*Ca\\v=s  -—the  volume  of  the  mean  grain,  the  weight  of  which  in 
pounds  is  w  :  then 

^vze;-i      27.68-  '^^vrd^. 


6        XII. — SARRAU'S  FORMULA  FOR  INTERIOR  BALLISTICS. 


qiiently  the  same  powder  may  be  quick  in  some  guns  and 
slow  in  others.     Chap.  XI.,  p.  24. 

When  y  >  0.273,  Equation  (A),  should  be  employed,  and 
conversely  for  Equation  (B).  The  two  equations  give  but 
little  difference  in  results  when  the  conditions  make  y 
approach  0.273. 

Referring  to  the  value  of  /?,  Equation  (3),  it  appears 
that  the  value  of  y  cannot  be  known  until  r  has  been  deter- 
mined. It  is  evident  that  the  methods  described  in  Chapter 
VIII  are  not  sufficiently  accurate,  so  that  the  following 
practical  method  is  adopted. 
Determination  of  Constants. 

A  well  defined  molded  powder  is  taken  as  a  standard  and 
its  values  of  /  and  r  accepted  as  unity.     For  this  powder 

the  values  of  a  and  (i,  Equations  (2,  3),  reduce  to  y  a  and  /, 
which  can  be  measured  by  the  means  described,  page  3. 

To  determine  the  value  of  M  in  equation  (A)  we  substi- 
tute the  value  of  F  obtained  as  the  mean  of  several  fires  in 
a  gun  in  which  the  standard  powder  is  relatively  quick,  and 
solve  with  respect  to  M. 

In  equation  (B)  we  proceed  similarly  for  A  and  B,  select- 
ing two  very  dissimilar  guns  and  taking  their  conditions  of 
loading  so  as  to  cover  as  wide  a  difference  of  limits  as  is  likely 
to  occur  in  practice. 

Choice  of  Formula. 

Inasmuch  as  the  values  of  A^  B,  J/,  are  true  for  all 
powders,  and  since  (Chapter  IX,  page  6)  the  force  of  all 
nitrate  powders  may  be  taken  as  constant,  and  in  this  case 
equal  to  unity,  equation  (A)  may  be  written 


--(0'(v)- 


S         1    ,1         8 


and  placing 


M^^^  =  X  (7) 


Xll. — {JARRAU'S  FORMULAE  FOR  INTERIOR  BALLISTICS.       7 


we  obtain 

r  =  «*/-3X«.  (8) 

If  this  value  of  r  substituted  in  that  of  y,  Equation  (6),  makes 
'y>  0.273,  Equation  (A)  may  be  used;  but  if  it  makes  y< 
0.273,  Equation  (B)  must  be  employed. 

To  determine  the  true  value  of  t  for  use  in  Equation  (B) 
requires  a  method  of  approximation  which  .s  too  long  to  be 
given  here,  but  can  be  found  in  the  works  mentioned  in  the 
bibliography.  This  will  not  generally  be  necessary,  as  the 
characteristics  may  be  determined  directly,  as  hereafter  ex- 
plained. 

The  value  of  r  for  the  standard  powder  is  approximately 
equal  to  the  time  of  its  burning  in  air  at  the  rate  of  about 
0.4  inch  (1  decimeter)  per  second.  Other  values  of  r  will 
therefore  have  approximately  their  values  in  air. 

Rejnark. — The  first  term  in  liquation  (B)  represents  the 
ideal  case  in  which  the  form  of  the  grain  is  such  that  the 
rate  of  conversion  (Note,  foot  page  2,  Chapter  X.,)  is  uni- 
form. The  second  term  is  sub  tractive  and  represents  the 
effect  of  the  decrease  of  the  rate  of  conversion,  or  of  the 
burning  surface,  when  the  grains  have  the  forms  required  in 
practice.  It  is  evidently  an  advantage  to  have  the  second 
term  as  small  as  possible. 

Empirical  Constants. 

The  numerical  values  of  A^  B,  M^  the  determination  of 
which  has  been  incidentally  described,  depend  only  upon 
the  units  of  measure  adopted  for  dimensions  and  masses. 

In  the  Ordnance  Department,  the  units  being  respectively 
the  inch,  for  internal  dimensions  of  guns;  the  foot,  for 
velocities  per  second,  and  the  pound,  the  constants  have 
the  following  values  given  by  their  logarithms : 

log  A  =  2.56635  ;  log  ^=  2.80964;  log  M=  2.84571. 

The  other  terms  in  the  formula  require  no  change ;  since 
the    effect  of  changes   in   the   units  by  which  the  different 


8        XII. — SARRAU's  FORMULA  FOR  INTERIOR  BALLISTICS. 

elements  of  loading  are  measured,  is  compensated  for  by  the 
numerical  value  of  the  empirical  constants. 

PRESSURE  FORMULA. 

The  following  equations  are  employed  to  determine  the 
pressures  on  the  base  of  the  projectile  and  on  the  base  of 
the  bore. 

p=Ka^£u  ( Ww)^d-\  (Q 

in  which  log  ^=3.96198. 

/o=^o «'  A  W^  wU-^,  (P) 

in  which  log  ^o=4.25092. 

Equation  (C)  is  obtained  by  differentiating  the  equation 
for  velocity  and  determining  the  maximum  acceleration  of 
the  projectile;  it  can  be  verified  only  by  the  apparatus 
described  Chapter  VII.  But  equation  (D)  can  easily  be 
verified  by  the  pressure  gauge.     See  Chapter  XI,  pp.  8 — 9 

PRESSURE  CURVES. 

In  designing  guns  it  is  indispensable  to  know  something 
about  the  pressure  at  other  points  along  the  bore  than  that 
at  which  the  maximum  pressure  occurs. 

In  Chapter  IX  we  have  considered  an  approximate  solu- 
tion; but  Sarrau's  formula  furnishes  us  a  method  which  is 
much  more  accurate. 
Expansion  Curve. 

If  in  equation  (B)  we  call 

J,=Aaw^\^-jP^j   f  (9) 

M.=BJ3^^>  (10) 

For  the  same  gun,  conditions  of  loading  and  powder, 
equation  (B),  becomes  by   writing,  v,  the  velocity  at  any 


XII. SARRAU'S  FORMUL/E  FOR  INTERIOR  BALLISTICS.       9 

point  of  the  bore,  for  F,  the  muzzle  velocity,  and  calling  u 
the  variable  length  of  travel  of  the  projectile. 

v^A^u\{\-B^u\).  (11) 

If  we  differentiate  equation  (11)  with  respect  to  v  and  u^ 
and  divide  by  dt^  we  have 

^  =  (|^,«-|-J/(,^,«-j)^  =/(«)$.      (12) 

in  which -y-  =  v  and  -^  =  acceleration  of  the  projectile,  or 
at  at 

dv      i)  7T  d^  <"" 

calling/,  the  variable  pressure  on  the  projectile ;  —=<-L- ^, 

From  this  follows 

Combustion  Curve. 

It  is  not  recommended  to  depend  upon  the  values  of  /, 

u 
thus  deduced  for  a  travel  of  the  projectile  of  less  than   ^  ; 

because  the  velocity  formula  is  not  considered  reliable  for 
such  small  values  of  u  as  those  existing  during  the  com- 
bustion period.     Chapter  XI  page  1. 

The  form  of  the  pressure  curve  in  the  initial  portion  may 
be  determined  as  follows. 

It  appears  from  the  following  table  based  upon  the  analy- 
sis of  Sarrau  that  the  displacement  of  the  projectile  corre- 
sponding to  the  maximum  pressure,  or  C/",  is  equal  to  0.6  Zy 
equation  (1).  This  gives  us  the  locus  of  this  pressure  and 
equation  (C)  gives  us  the  intensity.  It  remains  then  to  find 
the  form  of  the  portions  of  the  curve  in  the  neighborhood 
of  the  point  of  maximum  pressure.  This  is  obtained  from 
the  following  table  which  gives  the  proportion  of  the 
maximum  pressure  exerted  at  points  near  the  displacement, 
Uj  above.    In  this  table  the  variable  jo  represents  the  ratio 


10     XII. — SARRAU'S  FORMULAE  FOR  INTERIOR  BALLISTICS. 


u  d"^  y  •  • 

_,  and  — v^  values   proportional  to  the   acceleration,  since 
z  dx^ 

X,  in  this  case  represents  a  certain  function  of  /.     It  has  no 

connection  with  the  quantity  x,  on  page  3. 


TABLE    II. 


^0 

y^ 

JVo 

d^y. 

dx^ 

0.1 

0.180 

0.6 

0.710 

1.25 

0.651 

.3 

.605 

.7 

.705 

1.50 

.621 

.8 

.665 

.8 

.700 

1.75 

.590 

.4 

.693 

.9 

.692 

2.00 

.563 

.5 

.700 

1.0 

.680 

2.50 

.513 

That  is  to  say  that  after  the  projectile  has  travelled  over 
a  distance  equal  to  the  reduced  length  of  the  initial  air  space, 
the  pressure  is  -||-  of  the  maximum;  etc. 

It  is  supposed  that  the  pressure  on  the  wall  adjacent  to 
the  base  of  the  projectile  is  to  that  upon  the  base,  as  10  is 
to  7;  so  that  by  multiplying  the  pressures  just  determined 
by  1.43  it  is  easy  to  determine  the  probable  intensity  of 
the  corresponding  pressure  on  the  walls  of  the  bore. 

QUICKNESS  OF   POWDER. 

Sarrau  has  established  for  powders  fired  under  various 
conditions  of  loading  certain  moduli  of  quickness  which 
express  their  relative  quickness  under  these  conditions. 
See  page  5. 

The  modulus  of  a  powder  forms  an  important  independ- 
ent characteristic  which  is  of  considerable  help  in  establish- 
ing auxiliary  equations  of  condition  for  the  solution  of 
problems  in  Interior  Ballistics. 

It  may  be  shown  from  equation  (B)  that  if,  among  the 
variables  in  the  second  member,  r  alone  be  caused  to  vary, 
the  function,  F,  will  pass  through  a  maximum  state. 


XII. — SARRAU'S  FORMULAE  FOR  INTERIOR  BALLISTICS.      11 


In  practice  this  is  not  absolutely  true  ;  for,  as  already 
stated  in  Chapter  XI,  the  smaller  the  time  of  combustion, 
the  greater  the  number  of  volumes  of  expansion  in  a  given 
gun,  and  hence  the  greater  the  kinetic  energy  due  to  a 
given  charge. 

Equation  (B)  is  derived  by  a  process  of  approximation, 
and  its  physical  significance  cannot  therefore  be  rigorously 
interpreted.  It  serves  to  show,  however,  that  there  is  a 
limit  below  which  the  reduction  in  r  has  but  a  very  slight 
effect  upon  the  velocity,  and  which  it  is  inadvisable  to  pass; 
because,  as  r  diminishes  past  a  certain  point,  the  velocity 
increases  very  slowly;  but  the  maximum  pressure  very 
rapidly. 

The  value  of  r  corresponding  to  the  maximum  value  of 
Fis  obtained  by  placing  equal  to  zero  the  first  differential 
coefficient  of  the  second  member  of  equation  (B)  regarded 
as  a  function  of  r  and  solving  with  respect  to  r.* 

Denoting  this  value  of  r  which  is  called  the  time  of  the 
maximum  (velocity?)  by  Tj  we  have 

r.  =  3^((^.  (14) 

a 

In  a  given  piece  a  powder  behaves  as  a  slow  powder 
when  the  time  of  its  combustion,  r,  is  notably  greater  than 


*  Equation  B  may  be  written, 

V=C\p{t)=^CiT-\  —  RT-\\ 
in  which 

.=.£(i^  c=.  (/«)»(.„)»  (A); 

Hence 

—  =C(— ^r  2-\-\Rt    2) 


by  placing  —-  =0. 

a  T 


r,=.S^^SJ^'JKpl 


(U) 


12     XII. — SARRAU'S  FORMULi*:  FOR  INTERIOR  BALLISTICS. 


that  which  in  the  particular  arm  corresponds  to  the  theoret- 
ical maximum  of  velocity.  Further,  two  powders  fired  in 
different  pieces  should  be  considered  as  equivalent  as  far  as 
regards  quickness  if  their  times  of  combustion  are  propor- 
tional to  the  times  of  the  maximum  for  the  two  pieces 
employed.     Consequently  we  may  call  the  ratio 

^  =  ^  (15) 

the  modulus  of  quickness  under  the  particular  circumstances 
under  which  the  powder  is  fired ;  since  the  more  nearly  does 
Tj  equal  t,  the  more  nearly  does  q  approach  unity.* 

Under  this  view  we  may  adopt  the  following  arbitrary  scale 
for  the  classification  of  powders : 


TABLE 

III. 

Value  of  Modulus. 

Nature  of  Powder, 

1.0 

Very  quick. 

.9 

Quick. 

.8 

Medium. 

.7 

Slow. 

.6 

Very  slow. 

Since  the  above  classification  was  proposed  by  Sarrau,  it  has  been 
found  advisable  to  extend  the  value  of  the  modulus  in  both  directions. 
For  long  Sea  Coast  guns  it  now  runs  as  low  as  0.4,  while  it  has  been 
found  advantageous  in  the  B.L.  mortars  to  increase  it  to  1.3. 

In  any  case  we  have 

(W  u)^ 
q=^Bp^—^=dy.  (16) 

VELOCITY    AS    A    FUNCTION    OF    THE   MODULUS. 

By  introducing  q  in  place  of  r  in  equation  (B)  we  may 
obtain  a  new  and  useful  monomial  equation  of  the  general 
form 


*  The  modulus  of  quickness  also  is  designated  by  Sarrau  as  x. 


XII. — SARRAU'S  FORMULA  FOR  INTERIOR  BALLISTICS. 


13 


V=^A^,B)-^(l{y±^^  (17) 

in  which /(^)  may  be  taken  as  Nq^\  N  being  some  con- 
stant.*    See  page  28. 

Collecting  the  different  empirical  constants  under  one 
head,  which  we  may  call  M,  and  ascertaining  that  for  the 
particular  form  of  /  (q)  employed  we  have 

n  =  i^fZ^.;  (18) 

we  find  that  equation  (17)  reduces  to 

In  equation  (A')  V  varies  with  n\  that  is,  with  the 
modulus,  ^,  upon  which  by  equation  (18),  n  depends.  It  may 
be  used  as  an  approximation,  as  on  page  6,  by  giving  to  7t  a 
constant  value  under  conditions  of  loading  which  are  such 
that  the  modulus  is  comprised  within  certain  limits. 


*This  equation  shows  that  under  given  conditions  of  loading  the  initial 

//a\\ 
velocity  is  proportional  to  I  -y  I  . 

This  factor  is  called  the  ballistic  coefficient.  It  depends  both  upon  the 
force  of  the  powder  and  the  form  of  the  grain.  If  the  force  be  considered 
constant,  the  ballistic  coefficient  depends  only  on  the  form  of  the  grain. 

By  transforming  Equations  ( 2,  3)  we  have 

^  -T-J' 

It  will  be  observed  from  Equations  (C^),  (D^),  that  the  pressure  varies 
with  the  square  of  the  ballistic  coefficient.  This  relation  imposes  a  prac- 
tical limit  to  increasing  the  velocity  by  the  increase  of  this  coefficient. 

The  ballistic  coefficient  of  the  powder  must  be  carefully  distinguished 
from  the  ballistic  coefficient  of  the  projectile  to  be  hereafter  discussed. 


14    XII. — SARRAU*S  FORMUL.*^  FoR  tJJtERlOR  BALLISTICS. 


It  is  convenient  to  remember  that  n  increases  as  q  de- 
creases: when  ^=i\-,  ^=-J;  and  when  ^=3^,  n:=\* 

It  is  considered  that  these  are  the  limits  imposed  by 
practically  satisfactory  conditions  of  loading.  See  page  21. 
By  making  q—^  equation  (A')  reduces  to  the  form  of 
equation  (A),  which  was  thus  derived. 

Since  q—'6y  and  since  the  value  of  q=^  is  taken  to  be 
about  the  highest  modulus  that  can  be  profitably  employed, 
we  see  why  the  maximum  value  of  y  on  page  5,  has 
been  determined  =3^-^-3=0.273.* 

MAXIMUM    PRESSURE    AS   A    FUNCTION    OF    THE   MODULUS. 

By  substituting  for  -  in  the  value  of  a',  equation  (C),  its 
value  —  derived  from  equation  (14),  Sarrau  finds 

^=^(3^)-^^^(v)^.       (C) 

and  similarly 

A  =  ^o(3^r -/-(»^)  ^(v)  i-     («) 

PRINCIPLE  OF  SIMILITUDE. 

Two  guns  are  similar  when  all  their  homologous  linear 
dimensions  are  proportional  to  their  calibers.  Chapter 
XVI,  page  17. 

The  similitude  is  extended  to  the  loading  when  the 
weights  of  the  powder  and  of  the  projectile  are  proportional 
to  the  cube  of  the  calibers,  and  when  the  grains  of  powder 
have  the  same  form,  composition,  density,  etc.,  and   their 


^Although  not  so  named,  it  is  convenient  to  think  of  n  as  the  modulus 
of  slowness. 


Xlt. — §ARRAU*S  FORMULife  fOR  iNtEklofe  6aLUSTICS.     15 


dimensions  are  proportional  to  the  calibers.  Consequently 
the  numerical  coefficients  a^  /,  must  have  the  same  values, 
and  the  value  of  r  must  vary  proportionately  with  the  caliber. 

The  principle  of  similitude  enables  the  following  proposi- 
tion to  be  proved,  viz. : 

In  similar  gims,  similarly  loaded^  the  velocities  and  pressures 
corresponding  to  distances  passed  over,  which^  measured  ifi  cali- 
bers, are  equal,  are  respectively  equal  to  each  other. 

For,  let  us  consider  two  guns  having  calibers  respectively 

equal  to  d  and  to  d'  such  that  d'  z:^  B  d,  and  substitute  in 

d' 
Eq.  (16),  (17),  the  ratio  d  z=  —  raised  to  powers  varying  with 

d 

the  quantity  considered,  as  follows : 

From  the  conditions  of  similitude  we  have 

w:w' ::  W:  w^'::  d^ :  d'\ 


or 


7e>    -    W  ~  \  d    )  —^  ' 


u'         d' 
and  Ji  =  4_  =  6>. 

u  d 

In  Eq.  (17)  the  factors  A,  B,  A,  N,  and  the  ballistic  co- 
efficient will  be  eliminated  by  division,  so  that  substituting 

for  — |-  ,  (03)i  =  $1  and  so  on,  we  have 

I     q'  r 

Similarly  in  Eq.  (16)  since  /?  =r    --, zr  — j  Q. 


T  \  q' 

Now  if  T  varies  with  the  caliber,    —j-  =  —^,  and  —  =  1, 


T  ~"6I 


or  V=  V, 

Since  the  muzzle  may  be  taken  at  any  distance  the  propo- 
sition is  proved  as  to  velocities  and  can  be  shown  to  be  true 
as  to  pressures  by  the  similar  treatment  of  Equation  (C). 


16     XII. — SARRAU'S  FORMUL.^  FOR  INTERIOR  BALLISTICS. 


But  if  the  same  powder   is   used   in  two  similar  guns  of 

r  V  d'^ 

different  caliber — r-  =  1  and  -yit-  =  (QY  =  -7—. 
t'  V  d^ 

Consequently,  for  the  same  powder  in  similar  guns,  the  ve- 
locity varies  as  the  ^z**^  power  of  the  caliber. 

Equation  (D)  similarly  shows  that  when  the  same  powder 
is  used  in  similar  guns  the  pressure  varies  as  the  caliber. 

This  is  a  more  exact  explanation  of  the  practice  of  vary- 
ing the  size  of  the  grain  to  suit  the  gun  than  that  given 
Chapter  XI,  page  7. 


INFLUENCE  OF  THE  CONDITIONS  OF  LOADING 
UPON  VELOCITIES  AND  PRESSURES. 

General  Statement. 

Let  us  consider  as  constant  for  any  gun  the  quantities  d^ 
u,  IV,  and  as  constant  for  any  powder  its  force  and  form  of 
grain,  or/,  a  and  /,  i.e.,  its  ballistic  coefficient. 

The  quantities  which  may  then  be  varied  so  as  to  affect 
the  velocities  and  pressures  are  w,  A  and  r. 

There  are  an  infinite  number  of  sets  of  values  of  these 
variables  which  will  give  the  same  velocity  with  different 
maximum  pressures,  or  the  same  pressure  with  different 
velocities.  The  pressures  considered  are  those  upon  the 
breech  of  the  gun. 

The  following  practical  rules  result  from  differentiating 
the  Napierian  logarithms  of  the  above  named  variables  in 
Equations  (17)  and  (D').  In  equation  (17)  the  differential 
of  the  Napierian  logarithm  of  the  function  of  ^  which  it 


XII. — SARRAU'S  FORMULi^:  FOR  INTERIOR  BALLISTICS.      17 


contains  can  be  shown  to  reduce  to  the  form  * 

'^l0ge/(?)=-«^,  (19) 

and  in  equation  D', 

d\oz,q=  -—-;  (80) 


therefore 

d  V          dw          d  b.            dr 

dpo           dw       d  l\       d  t 
po    ~^   w     "^     A    ~r 

(21) 

(22) 

These  equations  enable  us  to  determine  the  variations 
in  velocity  and  pressure  corresponding  to  very  small  incre- 
ments of  the  variables  w,  A  and  r. 

The  influence  of  each  variable  on  the  value  of  the  velocity 
and  pressure  is  measured  by  the  coefficient  which  multiplies 
the  relative  variation  of  each  variable  in  the  above  equations. 

In  Equation  21  the  coefficients  of  , ,  and are 

respectively  §  ;  \\  n  =  ^  S^T^ ' 


bince  a  =  — ;    a^  = ==  —  (/  — 

^  r  T       T  T 

dq  dr 

Also  d  log.  f  (q)  =  d  loge  N  q-=J-S^L^ 

A/  q'^ 

d q^ n  q^~^       dq 

d  T 

=.11  d    loge   <]  = '' 

The  increments  here  discussed  are  small  finite  differences  made  in  ad- 
justing practically  the  conditions  of  loading.  For  considerable  differences 
Equations  (A,  B,  etc.),  should  be  employed. 


18      XIT. SARRAU'S  FORMULAE  FOR  INTERIOR  BALLISTICS. 

The  third  coefficient  varies  with  r  and  is  equal  to  0  for 
T  i^  Tj.  Its  value  increases  with  r,  but  does  not  exceed  ^ 
except  when  q  is  less  than  -^  which  is  not  likely  to  happen 
in  the  ordinary  conditions  of  practice. 

Comparing  equations  (21)  and  (22)  it  appears  that  while 
in  equation  (21)  the  variables  are  arranged  in  the  order  of 
their  relative  importance,  in  equation  (22)  the  influence  of 
w  on  the  maximum  pressure  is  less  than  that  of  A  or  r. 

Let  us  consider  as  a  fundamental  condition  that  the  maxi^ 
mum  pressure  remains  at  a  constant  value  determined  by  the 
strength  of  the  gun,  and  suppose  but  two  of  the  quantities 
Wy  A  and  r  to  vary  at  a  time,  the  third  remaining  constant. 

First  Case,     a  and  r  variable,  w  constant. 

The  equations  reduce  to 

d  t.        dt      ^ 

-^  =  —  and  (23) 


%'{^y-^      («) 


Therefore,  if  A  is  varied  by  changing  the  size  of  the 
chamber  for  a  given  charge,  the  time  of  burning  must 
change  correspondingly  to  the  density  of  loading.  In  such 
a  case,  if  ^>-5%,  T  increases  with  A.  Hence  the  conclu- 
sion: In  order  to  obtain  the  greatest  velocities  we  should 
use  high  densities  of  loading  and  slow  powder. 

Second  Case.   z£^  and  r  variable ;  A  constant.     (M.  L.  gun.) 

Equation  (22)  becomes  | = ,  (25) 

and  equation  (21)  ^  =  f  (J  -  «)  ^  ,  (26) 


*  That  is,  that  if  we  increase  w  by  10  per  cent ;  then,  to  fulfill  the  fun- 
damental condition,  r  must  be  increased  ^,  or  7.5  per  cent. 


XII. — SARRAU'S  FORMULi*:  FOR  INTERIOR  BALLISTICS.      19 

It  follows  from  equation  (18)  that  since  when  q  is  equal 
to  0,  «  =  J ;  and  that  when  q  is  greater  than  0,  n  is  less  than 
J,  the  factor  (J  —  n)  is  always  positive  and  therefore  that  the 
velocity  increases  with  the  charge  of  powder,  and  that  the 
maximum  pressure  will  not  be  exceeded  provided  that  the 
time  of  its  combustion  be  regulated  as  required  by  Equation 
(25). 

Third  Case,  w  and  r  variable  in  a  chamber  of  constant 
capacity.  We  have  supposed  in  the  preceding  cases  that 
the  volume  of  the  powder  chamber  can  be  increased  or 
decreased  at  will,  and  in  designing  guns  to  perform  certain 
work  the  conclusions  reached  are  useful.  Suppose  however 
that  we  desire  to  improve  the  conditions  of  loading  of  an 
existing  cannon.     In  this  case,  since 


A  = 

27.68  w           ,          d  t. 

wp  nivp 

dw 

(27) 

o                                   A 

and  therefore 

dV      ,dw         dr 

(28) 

dr          dw 

r  -*   w' 

(29) 

dV      ...         ^dw 

(30) 

in  which  (^— «)  is  positive. 

Therefore,  if  the  chamber  is  large  enough,  we  may  in- 
crease the  velocity  without  changing  the  pressure  by  using 
a  larger  charge  and  a  slower  powder. 

Examples. 
1.  Suppose  with  a  slow  powder  (;/  =  |)  we  wish  to  increase 

F  by  10  per  cent, -^  =  j^  .=  ^  =  ^  ^  ...  ^«,  = 
53.3  per  cent,  and =  —  53.3  =  93  per  cent.   That  is,  we 


20     XII. — SARRAU'S  FORMULAE  FOR  INTERIOR  BALLISTICS. 


would  use  nearly  double  the  charge  of  double  the  size  of 
grain ;  assuming  that  r  is  proportional  to  the  size  of  the  grain. 
2.  Using  a  quick  powder  {fi  =  g)  and 

~V  =  To  =  32"  loo  •'•  ^"^  ="  ^^  P"'  "'""''  ^"^  ~r  -=  ^^ 
per  cent.  Or  we  would  use  about  one-quarter  greater  charge 
of  less  than  one-half  greater  size. 

Fourth  Case,     w  and  A  variable  and  r  constant. 

This  corresponds  to  the  use  of  the  same  powder  in  guns 
having  different  chambers. 

From  the  conditions  we  have 

~  =  -i~'  (31) 

y=A'^-  (3.) 

That  is  to  say;  that  if  we  fix  the  size  and  shape  of  the 
grain,  and  wish  to  increase  the  velocity,  we  must  increase 
both  the  weight  of  the  charge  and  the  volume  of  the 
chamber. 

General  Remark, 

A  review  of  the  preceding  cases  shows  that  whenever  t 
varies,  F  is  a  function  of  n  and  also  of  either  wov  A  according 
to  which  one  of  these  is  variable. 

THE    EFFECT    UPON    PRESSURES   AND    VELOCITIES   OF 
VARYING    THE    TIME   OF   COMBUSTION. 

If  in  equation  (21)  we  allow  only  r  to  vary,  we  have 

_=-;._.  (33) 

The  value  of  n  increases  as  the  modulus  decreases;  conse- 
quently the  same  relative  variation  of  the  time  of  combustion 
has  a  greater  influence  upon  the  velocity  as  the  powder  be- 
comes slower.     See  Chapter  XI,  page  18. 


XII. — SARRAU'S  FORMUL/K  FoR  INTERIOR  BALLISTICS.     21 


(34) 


Now,  suppose  the  pressure  to  vary;  under  the  conditions 
equation  (22)  reduces  to 

dp^  _  _  ^^  . 

Combining  this,  with  equation  (33)  we  obtain  the  very  simple 
relation 

^=.^%.  (35) 

V  p^ 

which  expresses  a  relation  between  velocities  and  pressures 

similar  to  that  between  velocities  and  times  of  combustion,  in 

Equation  (33). 

It  has  been  stated  page  12,  that  the  values  -^  and  ^ 
may  be  considered  as  the  limits  that  the  modulus  should  not 
pass.  The  choice  of  these  limits  is  justified  as  follows. 
When  the  modulus  is  greater  than  -^  the  relative  variation 
of  the  velocity  depends  upon  n  in  equation  (35)  which  under 
these  circumstances  only  becomes  \  of  the  relative  variation 
of  the  maximum  pressure.  Consequently,  a  sensible  incre- 
ment of  the  velocity  is  obtained  only  with  a  considerable 
increase  in  the  pressure  and  the  energy  acquired  by  the  pro- 
jectile is  imparted  at  an  increased  risk  to'  the  gun.  This 
grows  less  as  the  modulus  diminishes  from  -^^  ;  because 
the  value  of  n  increases;  but  then,  from  Equation  (34),  the 
relative  variation  of  the  velocity  corresponding  to  the  same 
relative  variation  of  the  time  of  combustion  increases,  as 
shown  by  Equation  (33),  so  that  the  influence  of  accidental 
irregularities  of  the  powder  upon  the  velocity  continually 
grows  greater. 

It  is  then  advisable  to  fix  an  inferior  limit  for  the  modulus 
so  as  to  preserve  uniformity  in  velocity. 
APPLICATIONS. 

1.  To  determine  the  characteristics  a  and  y5  of  a  powder. 

The  most  practical  method  is  to  use  according  to  circum- 
stances either  equations  (A)  or  (B)  in  connection  with  equa- 


S^     Xlt.— SARRAu's  FORMULA  FOk  INTERIOR  BALLlStlCS. 

tion  (D),  and  to  substitute  in  these  equations  for  V  and  p^ 
the  mean  of  several  measured  velocities  and  pressures  ob- 
tained under  invariable  conditions  of  loading. 

We  have  then  two  independent  equations  involving  but 
two  unknown  quantities,  a  and  /?;  these  may  then  be  deter- 
mined without  reference  to  their  separate  factors. 

By  the  theory,  the  characteristics  are  entirely  independent 
of  the  gun.  In  this  respect,  and  also  in  that  they  give  us 
numerically  the  influence  of  all  the  elements  of  firing,  Sarrau's 
formulae  are  more  useful  than  those,  like  Noble's,  described 
in  Chapter  XI. 

Having  determined  accurate  values  for  the  characteristics 
of  a  powder,  we  may  compute  the  velocity  and  pressure  to 
be  expected  in  any  gun  whose  dimensions  are  known,  when 
the  conditions  of  loading  are  given;  and  conversely,  the 
dimensions  may  be  determined. 

Within  reasonable  limits  of  variation  of  the  quantities 
entering  them,  the  accuracy  of  the  formulae  has  been  abun- 
dantly verified. 

EXAMPLES. 

1.  To  find  the  characteristics  of  Du  Font's  P.  N.  (Brown 
Prismatic)  powder  from  a  single  firing  of  the  8  inch  B.  Iv. 
Steel  Rifle.     For  its  dimensions  see  Table  IV. 
Data.     2£/=110;  fr=  289;  A  =0.980 ;  z/=  1878; /„=  36000; 
^/  =  195.75.     Equation  (D)  gives  us 

«2= i^ — -  =0.9706=log-il.98704. 

An  application  of  the  test  mentioned  page  6,  will  show 
that  the  binomial  form.ula  is  applicable;  although  this  might 
be  assumed  for  powders  of  this  kind.  If  then  we  write 
equation  (B)  so  as  to  combine  in  each  term  the  quantities 
relating  to  the  gun  and  the  conditions  of  loading,  we  may 
reduce  it  to  the  form 


XII. — SARRAU'S  FORMULAE  FOR  INTERIOR  BALLISTICS.     23 


XF=a-a(3V  or    jS^"""^^, 

a  V 
in  which  Fis  measured  and 

—  =  — > (-  /v  and  Y= — ^^ -. 

Substituting  in  the  above  the  known  values  of  a,  X,  V 

and  K  we  find 

log  i3  =  1.33725. 

Another  method  is  to  fire  the  same  powder  under  very 
dissimilar  sets  of  conditions  in  which  W^  w,  u,  d  shall  have 
different  values  and  to  determine  the  values  of  V  under 
these  conditions. 

We  may  thus  obtain  two  formulae  of  the  form  of  the  above 
value  of  XV;  as  these  involve  but  two  unknown  quantities, 
the  characteristics  sought  may  be  determined. 

This  method  avoids  all  uncertainty  attending  the  oper- 
ation of  the  pressure  gauge;  but  the  former  method  is  gener- 
ally preferred  as  the  conditions  more  nearly  resemble  those 
of  practice,  and  introduce  the  customary  unit  of  measure- 
ment of  pressure, 

2.  To  compute  the  muzzle  velocity  to  be  expected  from 
the  8  inch  B.  L.  Steel  Rifle  for  the  preceding  powder. 
Data.     7i/=105;     A  =0.935;      /^=289. 


Computati( 
log  B        = 
log^        = 
log   W\    = 
log    u^       = 
log  d-'      = 

)n  of  y, 

2.30964 
1.33725 
1.23046 
1.14585 
1.09691 

Computatic 
log^        = 

log  a         = 
log    wt    = 
log   A^      = 
log  u^       = 
log   IV-^  = 
log  d-^    = 
log(l-;K)  = 
log    F        = 
V       = 

m  of   V. 
2.56635 

1.98704 
0.75795 
1.99276 
0.85939 

log  y 

y      = 

l-y= 

1.12011 
0.13186 
0.86814 

1.38477 
1.77423 
1.93859 

3.26108 
1824.3 

24     XII. — SARRAU'S  FORMULAE  FOR  INTERIOR  BALLISTICS. 

By  actual  measurement  Fwas  found  to  be  1825. 

3.  To   compute  the  maximum   pressure   on  the  breech 
under  the  same  conditions  as  in  No.  2.     But  with  a  powder 
{PO)  of  which  the  characteristics  are  different,  viz.: — 
a=log-il.97701;    y5=log-il.28978. 


log^o 

= 

4.25092 

log  a* 

= 

1.95401 

log   A 

= 

1.97102 

log  w^ 

= 

1.51589 

log    Wi 

= 

0.61523 

log  ^-2 

: 

2.19382 

log  A 

4.50089 

A 

= 

31688 

From  actual  firing  under  the  above  conditions  the  mean 
value  of  A  as  determined  by  two  independent  pressure 
gauges  was  31700  lbs. 

4.  In  order  to  avoid  injury  to  valuable  cannon,  it  is  custom- 
ary at  the  Proving  Ground  to  make  a  preliminary  trial  of 
new  powders  in  what  is  called  the  proof  gun. 
Data.     w=35.9;    «^=181;    A  =0.8988;    ^=8;  A=20420. 
Find  the  value  of  A  to  be  expected  when 

ze/=90;      «^=300;     A  =0.8018;     ^=8. 
The  first  set  of  data  give  in  Equation  (D), 
log  a2:=0.18085, 
hence,  we  find  for  the  second  set  of  data, 
A=41174  lbs. 
In  actual  firing  the  mean  value  was  found  to  be  41055  lbs. 

Useful  Tables. 

The  following  tables  give  the  dimensions  of  various  cannon 
of  the  U.  S.  land  service  with  the  characteristics  of  different 
powders  tried  in  them  and  the  resulting  pressures  and 
velocities  both  computed  and  as  verified  by  measurement. 


XII. — SARRAU'S  FORMULA  FOR  INTERIOR  BALLISTICS.      25 

They  will  be  useful  in  solving  problems  hereafter. 
Table  IV. 


Pow- 
der. 

Gun. 

d 
inches. 

u 

inches. 

W 

lbs. 

w 
lbs. 

A 

V 

feet  per 
sec. 

11  ^'' 
lbs.  per 

eq.   in. 

LX... 

3'^20B.  L.  rifle.. 

3.2 

73.2 

13 

3.50 

0.857 

1,649 

31,000 

LXB. 

....do 

3.2 

73.2 

13 

3.75 

0.827 

1,756 

35,150 

IKD.. 

....do 

3.2 

73.2 

13 

3.50 

0.857 

1,680 

29,100 

1KB.. 

....do 

3.2 

73.2 

13 

3.50 

0.857 

1,663 

30,  £^00 

KHC. 

12^^  mortar 

[2.0 

91.6 

610 

50.0 

0.821 

932 

22,000 

MW.. 

....do 

12.0 

91.6 

610 

48.0 

0  788 

959 

26,250 

EVF. 

S^^B.L.  R  Conv.. 

8.0 

98.5 

183 

45.0 

0.792 

1,488 

32,650 

PiV... 

8'^B.L.  R.  S 

8.0 

195.75 

289 

110.0 

0.980 

1,878 

36,000 

NM.. 

12'^B.L.R.C.L.. 

12.0 

273.5 

800 

265.0 

0.827 

1,688 

26,350 

NV3.. 

....do 

12.0 

273.5 

800 

265.0 

0.827 

1,718 

26,890 

NR... 

....do 

12.0 

273.5 

800 

265.0 

0.827 

1,826 

32,990 

NVi.. 

....do 

12.0 

273.5 

800 

265.0 

0.827 

1,760 

26,625 

NVa.. 

...do 

12.0 

273.5 

800 

265.0 

0.827 

1,756 

28,000 

IB... 

3^M7  M  L.R.W.I. 

8.175 

74.6 

10.5 

5.469 

0.814 

1,983 

25,000 

OB... 

12^^  mortar 

12.0 

91.6 

610 

52.0 

0.854 

987 

25,250 

oc... 

....do 

12.0 

91.6 

610 

52.0 

0.854 

942 

19,750 

26     XII. — SARRAU'S  FORMULAE  FOR  INTERIOR  BALLISTICS. 


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XII. — SARRAU'S  FORMULiE  FOR  INTERIOR  BALLISTICS.     27 


:  w 

:   t^ 


CO 

to 

^? 

w: 

<  • 
3.: 

o  • 


o  o 


CLP 


1-^       00 
to       i.. 

o  ; 


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o  p  Po  go  p  9jO 


pj  Fl  CL  p.  M  &.  p.  <j 


o? 


or- 


p-  p.  ^  p^  § 

<3 .     CO 


Kind  of 
powder, 


CO  CO  CC  p3  po  pO  CO  p3  p5  CO  CO  00  to  to  to  00  00  to  to  to  to  to 
I_L  'h-i  J-j.  i.o  to  to  to  to  to  to  to                to 
^^  -:i                                   CTi 
Or  Oi  Or     


I-*  to 
rfi.  >f>.  rf^  CO  CO  Ci  CO  CO  CO  CO  CO  OI  M-  Hi  M-  00  00  _M-  M-  h-i  CO  CO 

OS  OS  OS  to  to  OS  to  to  to  to  "to   OS  OS  OS  bi  bi  b>  os  bs  tf^^  br 


V-iOSOSOSM-r-i-OSOSOSOS-qf 
HJLM-(-J.M-l-iM.|-i-l-i|-'->-i-l-i-G0l-il-^i-i.QD00l-i.|-i-l-J.<X>Ol 

pp  pcocooococooicocooooococcooocoo 
bx  QT  br  "^ 


^ 


^3 


l-i  to 

COC^OTOTCT*»-Hf^rf^tO^OS 
Or  CT  Ol  (»  pO  CO  CO  CO  p3  CO  CO  Ol  to  O  to  O  Ol  00  Ql  OS  CI  Ol 

bo  bs  ht»"  ox  *-^  o  "-3  bi  br  bi  bi 

I-*- to  OS   CTl   OI 
CO  or  CO 


9°OOQOGOOO?DOOGOOOOOOOi:OQOQOOOOO-:i~3<It^«r>00 

o  CO  H-^  c;!  to  o  to  oi  oi  oi  c;i   oi  to  oi -^  «d  oc  co  to  to  to 

en  ^  j^i.  ,<j  ^  CO -^ -3  <}  •<} -3        rfi.  >-»■  rfi^  to  to  GO  CO -3  CD -q 

-*-  *  


--^ 


OcDi:o-^-3Ciososcno5Cscoi:Di:o?ociTh4i«'«0«oosrfi-^ 

OOSCOtOCrfM-COOSCOOCOOSOlCO^GOGOOTH-iQTOSOS 
00-3COOSOSOtOCOOCOOOOCOtOOCnOO'<l«DtOOl-»- 


to  M'M-h-lM-hJ^M.M.H'M-M.H*.  J^^  ^^^    ^ 

o'«o"co'^''-3'bT"^7  Oibl  or  OS  CO  «0  CD  CD  OtV  CD  CD  Os''>j^  -;^    ^ 
f-LOSCOM-C^OOOSlOCOCOGOCDCOQOOOOOajtOOt^OS   • 
OOOlCOCCOSI-»tOCOCDCOOOOCOtOOh-iOOCOOlM-OH-i 


lcotocococoto^oo^tototococototo      toto 

•  or  GO  O  O  O  CDCO)-^COtOCOOOtOOSCOOO»4^CO 


t0t-^O<{OO00O-QC»O0Srf^OC0OOO'<lG0fJ^M- 


CAStotococototococotoiocotototococototo      toco 

OCS  4^  OS  Ot  -3  cop  opp  Hi  Or  H-^  CTf  CCJ^sp^jfi-jCi  CO  tS 
O  Vj  Ot"bT"H-i"--3'*'<}bfl'^  o'h^'m-  O^lOCOOStO^CTtOOO 
OOiOOOtO— ■JCOOOOOOOlOtOCTCJOlOOO 

oooooooooooooooc;toooooo 


WfcStOOOOOC^tOCCM'COWOtOl-itOtOOTI-'t-AOOHiW 


j  Kumber  of  rounds 
considered. 


28     XII. — SARRAU'S  FORMULA  FOR  INTERIOR  BALLISTICS. 


DISCUSSION  OF  THE  COEFFICIENT  X^ 

If  in  Equation  (10),  Chapter  XI,  we  replace  r^  by  we 

4 

have  after  reduction,  r  =.  Tc^rr, — rr ji •> 

in  which  u  is  expressed  in  feet.  But  since  internal  meas- 
ures are  given  in  inches  we  may  avoid  errors  in  practice  by 
writing  this 

12 


in  which  G  =  nctAi\    2    • 
2240  g^  n 

If  in  Equations  (17)  and  (D^)  we  replace  the  ballistic  co- 
efficient by  C,  and  collect  the  constants  in  both  equations 
so  that 


3  (3  ^)W 3  ^  ' 

these  equations  will  read 

_^        ^C  wl  A^'  d^  td  N q""  ,^„. 

^  ="  ^ w^ •  ^  ^ 

^°==-^    Wi  did    '  (^^) 

Substituting  these  values  in  Equation  (36)  we  have 

X=Za  N^  q^--^    (-^y  (39) 

in  which  Z  =  ^-^  =  log-^  0.7394,  viz.,  5.488. 

The  factor  N,  which  in  Equation  (17)  was  taken  as  con- 
stant, is  not  absolutely  so.*    Its  value  is  given  in  Sarrau  as 

/(,)=iV,"  =  Z^i^>.  (40) 

By  substituting  the  value  of  N  impHed  in  Equation  (40)  in 

q  rt 

♦  For  values  of  f  between  yp  and   -^  ,iV"varies  only  from  1.012  to  1.056. 


XII. — SARRAU'S  FORMULAE  FOR  INTERIOR  BALLISTICS.     29 

the  factor  N*  /""'  in  Equation  (89)  and  calling  the  result- 
ing value  Q,  we  have 

This  reduces  Equation  (39)  to  ^ 

^  =  ^^'e(-|^)*.  (42) 

Discussion  of  the  Factors  of  X. 

Of  the  four  factors  producing  %'.  Z  is  a  constant ;  C 
depends  solely  upon  the  powder;  that  is  upon  its  force  and 
the  form  of  the  grain  ;  Q  depends  upon  the  suitability  to 
the  gun   and   projectile  of  the  kind  of  powder   employed ; 

—  j  depends  solely  upon  the  circumstances  of  the  particu- 
lar fire  considered.  Hence,  to  compare  the  intrinsic  proper- 
ties of  different  powders  fired  in  the  same  gun,  we  may 
compare  their  respective  values  of 

The  relation  between  ^  and  ^  is  shown  in  figure  2,  from 
which  it  appears  that  while  Q  is  sometimes  an  increasing  and 
sometimes  a  decreasing  function  of  q ;  for  values  of  q  be^ 
tween  fj^  and  -j^,  ^decreases  slowly  from  its  maximum  value 
of  1.245,  corresponding  to  ^  =  ^q,  to  a  value  of  1.159, 
corresponding  to  ^  =  -^j* 

If  the  force  of  all  nitrate  powders  were  truly  constant, 

C  =  —-  =  -jj-  would  depend  for  its  value  solely  upon  the 

form  of  the  grain ;  and,  since  within  ordinary  limits  Q  does 
not  vary  greatly,  we  would  expect  nearly  equally   good  re- 

*  From  this  we  may  conclude  that  for  ordinary  approximation  the  mean 
of  these  values,  or  ^  =  1.2  may  be  used.  Also  that  it  is  not  well  to 
depart  much  from  the  inferior  limit  of  g  established  by  Sarrau. 


30     XII. — SARRAU'S  FORMULAE  FOR  INTERIOR  BALLISTICS. 


suits  from  black  or  brown  prismatic  powder.  But,  in  the 
following  illustration,  taken  from  one  of  the  best  black  pris- 
matic powders  recently  tried,  we  find /to  be  so  small  that  C 
does  not  much  exceed  the  value  oP  3.0  deduced  from 
Table  I,  for  ordinary  powders  of  irregular  granulation. 

We  may  therefore  conclude  that  the  advantage  of  cocoa 
powder  consists  in  its  maintaining  its  force  at  nearly  unity* 
without  becoming  so  quick  (or  slow ;  figure  2)  as  to  cause  its 
value  of  Q  to  become  unduly  small.  These  considerations 
indicate  in  a  general  way  that  its  peculiar  properties  are  due 
to  the  nature  of  the  fuel  it  contains. 

Illustrations. 

The  following  data,  derived  from  experimental  records, 
illustrate  the  principles  discussed : 

COMPARISON    OF    POWDERS. 

Gun Sin.  B.L.R.  8in.B.L.R. 

Powder,  kind Bl.  prism.  Br.  prism. 

Powder,  name O.  I.  N.  Ger.  cocoa. 

W. 45.0  289.0 

Sph.  Density 2.9  4.5 

V, 1852  1875 

A 33075  35900 

u 119.8  195.75 

a 1.5  1.5 

/  1  ^ 

* ^  3 

a" 2.45  0.93 

(i 0.78  0.21 

/. 0.70  0.96 

r 0.43  1.59 

C 3.16  4.45 

q 0.70  0.38 

*  See  Table  V,  in  which  the  last  six  powders  are  cocoa* 


Xli. — gARRAU*S  FORMUL.fi  FOR  INTERIOR  feALLtSTICS.     SI 


Q 1.23  1.12 

X  observed 28.28  34.32 

X  Equation  (40) 28.44  34.87 

n 21.26  27.39 

Ratio  of  n 1.00  1.29 

If  we  exchange  powders  only,  we  have — 

Powder Ger.  cocoa.  O.  I.  N. 

q 0.19  1.47 

Q 0.73  0.50 

II 17.95  8.55 

Ratio  of  n 2.10  1.00 

That  is,  that  while  each  powder  is  best  suited  to  the  gun  in 
which  it  is  actually  used,  the  cocoa  powder  would  be  better 
for  general  use,  and  might  profitably  be  adapted  to  the  siege 
rifle  by  reducing  the  size  of  the  prism  so  as  to  diminish  r  and 
increase  Q. 

MAXIMUM  VALUE  OF  X, 

The  value  of  11  before  deduced,  enables  us  to  solve  some 
very  important  problems  in  internal  ballistics. 

As  an  example,  let  us  consider  the  question  of  how,  with 
our  present  knowledge  of  gunpowder,  we  may  attain  the 
maximum  value  of  X'  Also,  let  us  apply  this  to  a  gun  the 
construction  of  which  limits  p^ ;  the  spherical  density  of  the 
projectile  being  known  and  the  value  of  ?/  being  expressed 

8  IV 
in  terms  of  the  caliber  or  //  rr  n  d,     Let  s  =  — -—    be  the 

spherical  density  of  the  projectile.^  The  maximum  value 
of  C^  being  4.5,  figure  2  shows  that  the  maximum  value  of 
IT,  and  hence  of  x^  will  require  ^  =  0.6. 

The  maximum  value  of  tj  will  depend  on  that  of  A.    The 

*  See  Chapter  XVI,  page  6. 


82     Xn. — SARRAU*S  FORMULi^  FOR  INTERIOR  SAlLISTICS. 

specific  gravity  of  some  powders  is  now  such  that  a  value  of 
A  =:  1,  has  been  reached.  We  may  consider  this  a  maxi- 
mum, as  it  is  rarely  exceeded.  After  deducing  general  equa- 
tions, we  will  apply  them  to  a  typical  gun  based  on  the  8-in. 
B.  L.  R.  Steel,  in  which  j  =z=  4.5 ;  ^/  =  24,  and  take  the 
maximum  value  for  /„  as  36000  lbs.  per  square  inch,  that 
being  what  the  records  indicate  to  be  a  desirable  limit. 

1.  Proper  Weight  of  Charge. 

By  substituting  the  values  assigned  for  JV,  A,  d,  t^,  q  in 
Equation  (D'),  it  leads  to  the  following  ratio : 

^=[log"'n.lll9^']S  (44) 

In  which,  by  substituting  the  special  typical  values  assumed 
for /(J,  n  and  i",  we  have  w  =  0.2  W. 

In  the  8-in.  rifle  this  would  reduce  the  charge  of  powder 
about  one-half. 

2.  Proper  Size  of  Grain. 

If  in  Equation  (16)  we  place  q  =s  0.6  and  assign  values  as 
above,  we  have  for  a  general  equation,  since  /  =  J 

r  =  log "  ^2.0799  (^s  n)h  d.  (45) 

This  shows  that,  as  before  stated,  the  size  of  the  grain 
should,  in  similar  guns,  vary  directly  with  the  caliber.  For 
the  8-in.  rifle,  this  makes  %  =  1.0,  or,  from  the  preceding  table, 
the  size  of  the  grain  should  be  about  68  fo  of  its  present  linear 
dimensions;  the  force  of  the  powder  being  unity,  and  the 
form  remaining  unchanged. 

3.  Maximum  velocity. 

The  maximum  value  of  H  =  5.488  X  4.5  X  1.245  =  30.73. 

But  U  =  X  \  wA    =  x-:7a 3-   =  30.73. 

By  substituting  the  value  of  wl  deduced  from  Equation  (44) 


XII. — SARRAU'S  FORMULA  FOR  INTERIOR  BALLISTICS.     33 

and  reducing,  we  have* 

V=  Tlog-^  2.7355  ^^  ]'      '  (46) 

Which  in  the  type-gun  gives 

F=  1716,  or  ;^=:  46.48. 
The  largest  value  of  %  Y^^  attained  with  this  gun  is  about 
35.0 ;  showing  an  efficiency  of  about  80  per  cent. 

Remark. 

For  sea  coast  guns,  in  which  the  bulk  and  weight  of  the 
charge  is  of  no  special  consequence,  since  the  guns  are  sta- 
tionary and  magazine  room  is  ample ;  the  waste  of  the  powder 
and  the  increased  volume  of  the  chamber  necessitated  by  the 
present  use  of  very  large  charges  may  be  neglected  in  favor 
of  the  high  muzzle  energies  required.  But  as  the  caliber  of 
the  gun  decreases,  and  its  mobility  increases,  the  necessity  for 
reducing  the  weight  of  the  charge  becomes  more  important. 
This  is  especially  true  in  the  loading  of  magazine  small  arms, 
the  efficiency  of  which  requires  the  weight  of  the  ammuni- 
tion to  be  reduced  to  a  minimum ;  so  that  the  number  of  cart- 
ridges that  the  soldier  may  carry  will  be  as  great  as  possible. 

*  This  is  independent  of  the  caliber  as  would  be  expected  from  the 
principle  of  similitude,  x  may  also  be  shown  to  be  independent  of  the 
caliber,  by  substituting  values  of  W  and  w  in  terms  of  s,  and  of  «  in 
terms  of  d. 


XIII. — HISTORY    OF    GUNPOWDER. 


CHAPTER    XIII. 

HISTORY  OF  GUNPOWDER. 

Origin. 

Knowledge  of  the  properties  of  nitre  as  a  supporter  of 
combustion  are  attributed  to  the  accidental  kindling  of  the 
embers  of  a  camp  fire  by  the  salt,  often,  in  India,  found  effer- 
escent  upon  the  surface  of  the  ground.  As  sulphur  is  not 
essential,  its  first  employment  cannot  be  conjectured.  For 
its  binding  properties  honey  was  used  at  an  early  date. 
Early  Use. 

The  use  of  gunpowder  was  at  first  confined  to  fireworks 
and  rockets.  These  are  mentioned  in  Chinese  records  over 
2000  years  old,  and  seem  to  be  indicated  in  the  account  of 
Alexander's  invasion  of  India  at  about  the  same  epoch. 

The  transition  from  its  use  in  a  paper  tube,  or  bamboo 
cane,  to  cannon  of  different  sizes  is  indicated  by  the  etymology 
of  the  latter  name.     The  barrel  of  any  fire  arm  is  in  French 
called  canon. 
Early  Cannon. 

The  first  use  of  gunpowder  as  an  agent  for  propelling  pro- 
jectiles is  assigned  to  the  Moors  at  the  siege  of  Baza  in  Spain, 
about  1325;  twenty-one  years  before  the  battle  of  Crecy. 
This  is  about  the  time  that  the  chemist  monk,  Berthold 
Schwartz,  of  Freiburg,  is  said  to  have  discovered  its  pow- 
ers by  the  accidental  ignition  of  a  ternary  mixture,  lying  in 
a  mortar  and  covered  with  a  stone. 

Owing  to  the  weakness  of  the  early  cannon — which  were 
constructed  after  the  manner  of  ordinary  barrels,  sometimes 


XIII.— HISTORY   OF    GTJNPOWDER. 


of  iron  bars  welded  together  longitudinally  and  hooped  with 
iron  tires,  and  sometimes  even  of  wood,  wrapped  with 
rope — efforts  at  first  were  directed  to  reducing  the  strength 
of  the  new  agent. 

Early  Powder. 

Therefore,  although  the  best  proportions  had  long  been 
known,  it  was  often  composed  of  equal  parts  of  the  three 
ingredients,  and  sometimes  mixed  with  saw-dust,  resin,  sand, 
or  ashes. 

It  was  often  mixed  and  ground  by  hand  as  required,  and 
was  used  in  the  form  of  a  fine  meal  or  powder^  from  which 
its  name  is  derived. 

The  diminished  velocity  of  inflammation  resulting  from 
the  use  of  meal  powder  favored  the  end  in  view;  but,  since 
the  cartridge  was  yet  unknown,  the  condition  of  this  powder 
made  it  so  inconvenient  to  load  the  long  guns  then  used 
that  the  efficiency  of  artillery  was  much  impaired. 

Early  Breech-loaders. 

To  overcome  this  difficulty  in  loading,  cannon  at  a  very 
early  date  were  made  to  load  through  the  breech.  But  the 
arts  at  that  time  afforded  no  means  of  preventing  the  escape 
of  gas  through  the  joint  so  formed,  and  such  cannon  are 
comparatively  rare. 

It  will  be  seen  hereafter  that  the  practical  utilization  of 
this  principle  depended  upon  the  discovery  of  the  self-sealing 
gas  cheeky  the  best  form  of  which  exists  in  the  metallic 
cartridge  case,  now  used  for  small  arms. 

But  for  this  essential  improvement  m^any  of  the  systems 
now  In  vogue  are  but  repetitions  of  these  ancient  forms,  not 
only  in  principle,  but  in  many  details  of  construction  aad 
operation. 

The  reciprocal  evolution  of  the  gun  and  its  ammunition 
is  a  striking  illustration  of  the  law  of  continuity. 


Xllf. — mSTORV   OF   rttlKfOWDER. 


Men  have  probably  always  been  equally  ingenious  in  util- 
izing the  accumulated  capital  of  knowledge  at  their  com- 
mand; but  the  successful  application  of  even  simple  princi- 
ples requires,  in  many  cases,  the  parallel  development  of 
apparently  unrelatec  arts. 

Intermediate  Stage. 

It  was  not  until  near  the  close  of  the  16th  century  that 
cannon,  first  of  copper  or  its  alloys,  and  then  of  cast  iron, 
were  made  strong  enough  to  resist  the  pressures  due  to  the 
use  of  the  grained  powder,  the  use  of  which  had  hitherto 
been  confined  to  muskets.  This  was  called  corned  powder, 
vide  pepper-corn  J  barley-cornj  coming-mill. 

Until  about  the  middle  of  the  present  century  no  great 
improvement*:  occurred  in  gunpowder  or  in  cannon.  The 
reasons  for  this  were  the  general  assumption  that  gun- 
powder was  instantaneously  converted  into  gas,  and  the  want 
of  any  apparatus  for  measuring  pressures. 

Use  of  Eprouvette. 

Gunpowder  was  proved  by  firing  it  from  the  Eprouvette,  a 
small  mortar  with  its  axis  carefully  fixed  at  an  elevation  of 
45*.  The  quality  of  the  gunpowder  was  determined  by  the 
distance  to  which  an  accurately  fitting  ball  of  a  given  weight 
was  thrown  by  a  given  weight  of  powder.  Although  some 
difference  existed  in  the  size  of  the  grain  used  in  different 
juns,  the  proof  7'ange  increased  as  the  size  of  the  grain  dimin- 
ished; so  that  for  large  guns  the  size  of  the  grain,  as  meas- 
ured by  our  present  standard,  was  exceedingly  small.  See 
Chap.  XI. 

Rodman's  improvements. 

1.  Pressure  Gauge. 

The  late  General  Rodman,  of  the  United  States  Ordnance 
Department,  was  the  first  to  investigate  the  properties  of 
gunpowder  in  the  modern  method. 


3tm.— tttStOkV  Of  6tlNl>6Wt)£R. 


His  experiments,  conducted  with  the  view  of  increasing 
the  effectiveness  of  the  system  of  cannon  which  bears  his 
name,  depended  primarily  upon  his  employment  of  the  pres- 
sure gauge.  This  was  a  pyramidal  indenting  tool,  previously 
used  by  him  to  test  the  relative  hardness  of  cannon  metals, 
and  applied  in  the  manner  indicated  for  the  crusher  gauge. 

Although  open  to  many  grave  objections  of  detail,  this 
instrument  gave  useful  relative  results  and  served  to  draw 
attention  to  the  very  erroneous  estimates  previously  made  as 
to  the  pressure  exerted  by  gunpowder.  When  fired  in  its 
own  volume,  this  had  been  variously  estimated  at  from  0.7 
to  700  tons  per  square  inch. 

2.  Powder. 

a.  Mammoth. 

Rodman's  first  step  was  to  recommend  the  use  of  large 
charges  of  "mammoth  "  powder,  which  was  of  about  three 
times  the  diameter  of  the  largest  powder  previously  used. 

This  gave  satisfactory  velocities  and  moderate  pressures; 
and,  since  its  manufacture  required  less  granulation  than 
before,  it  was  cheaper,  pound  for  pound. 

b.  Perforated. 

About  1860,  he  improved  upon  this  idea  by  suggesting 
the  use  of  perforated  powder,  made  for  small  cannon  in 
cylindrical  cakes,  and  for  larger  cannon  in  hexagonal 
prisms  which  could  be  built  up  into  cartridges. 

Owing  to  the  great  cost  and  novelty  of  this  powder,  and 
to  the  intervention  of  the  civil  war,  the  perforated  powder 
was  used  in  this  country  only  for  experiments ;  but  the 
mammoth  powder  has  until  lately  been  exclusively  used  for 
heavy  guns. 

DERIVATIVES    FROM    RODMAN's    POWDER. 

Russian  Powder. 

The  perforated  prisms  were  experimented  with  in  Russia, 
from    1860-1865,  being    finally   made    much    smaller    than 


btllt. — kistORY   OF    GUNPOWDEfe. 


Rodman's,  and  pierced  with  seven  small  holes.     The  powder 
was  so  made  in  order  to  adapt  it  to  the  muzzle  loading  guns 
then   used.     See    Fig.   IB,    Chap.    IV.     This   is   known   as 
/Russian  prismatic  powder. 
English  Powders. 

The  English  objected  to  this  powder,  saying  that,  owing 
to  the  number  of  perforations  it  contained  and  to  its  dimin- 
ished density,  it  was  liable  to  break  up  in  the  gun. 

About  1875,  they  returned  to  General  Rodman's  original 
idea,  adopting  the  cubical   Pebble  powder,  the  cubes,  for 
the  largest  gun  ,  being  about  lYz  inches  on  the  edge. 
United  States  Powders. 

In  the  United  States,  the  mammoth  powder  was  im- 
proved upon  by  the  adoption  about  1873  of  the  Du  Pont 
Hexagonal  powder.  Fig.  12,  Chap.  IV. 

This  and  the  Sphero-Hexagonal  powder,  Fig.  12,  have 
the  advantage  of  great  uniformity  in  the  size  and  shape  of 
the  grains  and  in  the  form  of  the  interstices  between  the 
grains.  They  are  also  progressive,  owing  to  the  diminished 
density  of  the  interior  of  each  grain. 

This  results  from  the  fact  that  the  effect  of  compression 
is  not  transmitted  homogeneously  throughout  the  mass 
compressed.  The  density  is  always  greatest  next  to  the 
moving  surface. 

For  reasons  given  in  the  text.  Flat  powders  of  the  Z.  X. 
type.  Fig.  12,  are  also  occasionally  used. 
Italian  Powder. 

The  Fossano  powder,  made  in  Italy,  consists  of  an 
agglomeration  of  dense  grains  of  medium  size,  set  in  a 
mass  of  powder  meal  and  pressed  to  a  density  less  than 
that  of  the  individual  grains.  Its  operation  is  distinctly 
progressive. 

The  principle  is  applied  to  other  powders,  both  molded 
and  of  irregular  granulation. 


Xin. — HISTORY   OF   GUNroWDER 


MODERN    POWDERS. 

In  order  to  obtain  the  most  effective  combination  of  gun 
and  powder,  each  type  of  gun  now  requires  a  special 
powder,  and  some  cannon,  as  mortars,  require  more  than 
one  powder  for  each  mortar.  This  increases  greatly  the 
difficulty  of  supply. 

The  kind  of  powder  best  suited  to  each  type  of  gun  is 
still  (in  1888)  undergoing  experimental  investigation. 

The  advantage  of  adapting  the  size  of  the  grain  to  the 
size  of  the  gun,  upon  which  for  simplicity  so  much  stress 
has  been  laid,  is  becoming  of  diminished  importance,  since 
the  effects  due  to  increased  size  may  be  attained  in  many 
other  ways. 

Owing  to  the  great  number  of  conditions  which  require 
to  be  simultaneously  satisfied,  including  the  effect  of 
meteorological  conditions  prevailing  during  manufacture, 
the  powder  makers  find  it  difficult  to  meet  the  increasing 
exactness  of  the  demands  made  upon  them.  This  applies 
even  to  the  duplication  of  satisfactory  samples. 

Present  Custom. 

All  large  guns  of  the  present  day  use  hexagonal  prisms 
like  the  Russian  prismatic,  but  pierced  with  a  single  hole. 
This  is  easier  to  make  and  its  ballistic  properties  are  better. 

It  is  preferably  a  concrete  powder  made  by  consolidating 
under  pressure  small  grains  of  powder  previously  com- 
pressed in  the  ordinary  manner.  Mealed  powder  is  some- 
times used  instead  of  that  which  has  been  grained. 


XIV. HIGH    EXPLOSIVES. 


CHAPTER   XIV. 

HIGH   EXPLOSIVES. 
Classification. 

Except  the  chlorate  mixtures,  the  high  explosives  used  in 
warfare  are  all  organic  nitro-substitution  compounds,  gener- 
ally of  the  third  order,  in  which  3  atoms  of  H  are  replaced 
by  3  molecules  of  NOg. 

The  most  important  are  Gun-cotton,  Nitro-glycerine, 
and  their  derivatives.  The  derivatives  of  picric  acid  are 
growing  in  importance,  and  so,  for  special  purposes,  are  the 
mono-,  di-,  and  tri-nitro-benzines  and  naphthalines. 

Those  which  in  their  operation  resemble  the  mercuric 
fulminate  are  C2i\\t6.  fulminating  compounds,  and  include,  be- 
sides their  typical  salt,  the  mixtures  in  which  the  chlorates 
are  used  dry. 

The  demands  of  civil  engineering  and  the  hope  of  success- 
fully adapting  these  explosives  to  warfare  are  constantly  in- 
creasing the  number  of  those  for  which  both  safety  and 
efficiency  are  claimed.  On  the  other  hand,  many,  once 
famous,  are  obsolete,  so  that  the  following  discussion  will 
relate  only  to  those  of  which  long  experience  has  demon- 
strated the  essential  properties,  and  to  the  most  distinguished 
of  recent  competitors  for  the  selection  of  the  engineer, 
Danger. 

Although  their  composition  and  violence  render  the  hand- 
ling of  many  as  compared  with  gunpowder,  dangerous;  yet, 
a  knowledge  of  their  properties  is  demanded  b-  the  con- 
ditions of  the  time;  and,  as  with  gunpowder  and  steam,  this 
knowledge  comes  principally  by  experience. 


XIV. — HIGH    EXPLOSIVES. 


The  disasters  reported  with  such  apparent  frequency  are 
the  price  of  progress  toward  safety,  and  point  rather  to  the 
enormous  consumption  of  these  explosives,  often  by  ignorant 
and  reckless  persons,  than  to  any  necessary  peril  when  proper 
precautions  are  observed. 
Commercial  Importance. 

The  scale  on  which  these  explosives  are  employed,  prob- 
ably, as  with  gunpowder,  much  greater  in  time  of  peace 
than  in  war,  appears  from  the  size  of  blasts  fired  almost  daily 
in  the  Californian  mines  during  the  period  of  their  greatest 
activity.  These  blasts  often  contained  50,000  pounds 
apiece. 

The  great  blast  at  Hell  Gate,  New  York  Harbor,  in  1885, 
contained  but  six  times  as  much. 

The  economic  value  of  an  explosive  depends  so  much  upon 
the  net  cost  of  the  work  performed  that  it  is  interesting  to 
note  the  following  relative  scale  of  prices  per  pound  in  1888. 


Explosive, 

Price. 

Proportion. 

Gunpowder, 

20  eta. 

1.0 

Dynamite, 

50 

2.5 

Nitro-glycerine, 

80 

4.0 

Gun-cotton, 

1.00 

5.0 

COMMON  PROPERTIES  OF  GUN-COTTON,  NITRO- 
GLYCERINE, AND  THEIR  DERIVATIVES.* 

Sensitiveness. 

When  not  freed  from  the  acids  used  in  their  manufacture, 
these  explosives  are  prone  to  spontaneous  decomposition 
and  tend  to  form  products  of  a  lower  order  of  substitution. 

While  undergoing  decomposition,  their  sensitiveness  is  in- 
creased, but  their  efficiency  when  exploded  is  diminished. 

When  properly  prepared,  they  are  not  sensitive  to  moderate 


*  Cadets  are  advised  to  review  the  articles   in  the   Chemistry  which 
treat  of  nitro-glycerine  and  gun-cotton. 


XIV. — HIGH    EXPLOSIVES. 


shock;  but  friction,  the  impact  of  a  projectile,  or  the  shock 

of  discharge  may  cause  their  explosion. 

Firing. 

As  a  rule,  they  all  explode  at  about  200°.  When  ignited 
by  a  flame  and  unconfined,  they  burn  more  or  less  quietly. 
If  confined,  their  explosion  is  of  a  low  order  unless  they  are 
detonated.  Their  behavior  in  this  respect  depends  much 
upon  their  mass  and  the  resistance  of  the  envelope.  See 
Chap.  II. 

They  possess  the  remarkable  property  of  exploding  vio- 
lently  when  gradually  heated  to  about  200°;   whereas,  if 
'dropped  upon  a  red  hot  iron,  they  may  simply  deflagrate. 
Detonation, 

Owing  to  the  variety  of  the  means  by  which  the  mercuric 
fulminate  may  be  ignited  and  to  the  nature  of  its  product, 
it  is  almost  exclusively  employed  for  detonation,  preferably 
alone  and  pure,  and  sometimes  with  a  primer  of  dry  gun- 
cotton. 

The  detonators  are  commercially  known  as  blasting  caps^ 
exploders^  or  fuzes  of  various  degrees  of  "force  "  according 
to  the  quantity  of  fulminate  they  contain.  The  fulminate 
lies  in  a  thin  copper  tube,  one  end  of  which  is  closed,  and  is 
ignited  either  by  a  quick-match  or  by  the  heating  of  a  fine 
platinum  wire  by  the  electric  current.  The  detonator  is 
placed  in  immediate  contact  with  the  charge,  but  should  be 
so  disposed  that,  if  the  quick-match  is  used,  the  charge  shall 
not  be  prematurely  ignited. 

The  mass  of  the  fulminate  should  bear  a  certain  ratio  to 
the  mass  and  condition  of  the  explosive;  this  may  neutralize 
the  advantages  on  the  score  of  safety  which  the  sluggishness 
of  the  explosive  confers. 

Long  charges  may  require  to  have  dispersed  through  them 
several  detonators  in  order  to  maintain  the  energy  of  the 
explosive  wave. 


XIV. — HIGH    EXPLOSIVES. 


Products. 

Except  Nitro-glycerine  all  the  substitution  compounds 
yield  a  large  amount  of  CO,  and  hence,  where  potential  is 
sought,  require  the  addition  of  an  oxydizing  agent. 

Pressures. 

The  ordinary  gauge  being  unsuited  to  measuring  the  high 
pressures  of  detonation,  special  devices  have  been  contrived. 

General  Abbott  of  the  U.  S.  Engineers,  in  a  series  of 
experiments  (which  bear  to  the  high  explosives  the  same 
relation  as  do  Noble  and  Abel's  experiments  to  gunpowder), 
suspended  in  water  his  gauges  at  definite  distances  from 
the  submerged  explosive. 

For  experiments  in  air,  charges  of  given  weights  are 
detonated  either  within  or  upon  similar  blocks  of  lead  and 
the  resulting  deformations  compared.  Or  the  exact  charges 
required  to  burst  similar  hollow  projectiles  may  be  deter- 
mined. 

Effects. 

General  Abbott's  experiments  give  the  following  scale  by 
which  to  measure  the  force^  Chap.  II,  of  explosives.  His 
results  apply  only  to  sub-aqueous  mining  and  indicate  the 
paradoxical  fact  that  Dynamite  is  more  powerful  than 
Nitro-glycerine. 

He  found  that  the  pressures  registered  by  a  crusher  gauge 
varied  as  the  Yi  power  of  the  charge  and  inversely  as  the 
1.4  power  of  the  distance.  Or  calling  /  the  pressure,  %v  the 
weight  of  the  charge,  d  the  distance,  and  k  a  constant  vary- 
ing for  each  explosive  and  for  the  nadir  angle  under 
water. 


3  //  kw\* 


These  comparative  results  are  expressed  by  the  following 
table: 


XIV.— HtGtt  EXPLOSIVES. 


Nitro-glycerine,  81  0.93 

Gun-cotton,  87  1.00 

Dynamite,  100  1.15 

•  Explosive  Gelatine,      117  1.35 

a  result  quite  different  from  that  of  Chap.  II. 

On  the  other  hand,  extended  practice  in  mining  operations 
under  ground  confirms  the  relative  useful  values  of  the  high 
explosives  as  determined  by  their  potentials  and  stated  in 
Chap.  II. 

Three  spheres  surround  the  center  of  the  explosion: 

1.  The  sphere  of  pulverization. 

2.  The  sphere  of  rupture  or  dislocation. 

3.  The  sphere  of  fracture  or  fissure. 

The  relative  dimensions  of  these  spheres  vary  with  the 
force  and  potential  of  the  explosive. 
Tamping. 

The  great  rapidity  of  the  reaction  renders  special  tamping 
unnecessary,  since  the  pressure  of  the  atmosphere  suffices  to 
produce  many  of  the  effects  desired.  This  is  the  origin  of 
the  common  idea  that  such  explosives  act  downward.  This 
property  is  particularly  valuable  in  military  operations  where 
time  is  precious. 

The  best  results,  however,  are  found  when  they  are 
tamped.  Even  a  thin  layer  of  earth  or  water  greatly  in- 
creases their  effect.  For  a  similar  reason  the  mass  of  the 
charge  is  best  placed  between  the  detonator  and  the  object 
to  be  destroyed. 

Example. 

Long  iron  tubes  filled  with  dynamite  have  been  detonated 
in  air  without  converting  all  of  their  contents.  When  the 
tubes  were  submerged,  the  entire  charge  was  detonated, 
Chap.  II,  page  5.  The  accidental  explosion  of  charges  which 
have  been  imperfectly  detonated  leads  frequently  to  disaster, 
and  so,  it  may  be  said,  does  tamping  with  an  iron  bar. 


XIV.— tttGli  eX!>L6S1VES. 


Physical  Condition. 

The  greater  the  density  of  the  explosive  the  smaller  the 
bore  hole  required  to  receive  it,  and  hence  the  greater  its 
economy. 

Plastic  explosives  are  valuable  since  they  may  be  used  in 
irregular  cavities,  and  in  those  opening  downward;  they  may 
also  be  rammed  after  loading  so  as  to  increase  the  value  of  A . 

The  advantages  in  this  respect  of  the  liquid  state  of  nitro- 
glycerine made  it  very  popular  at  first;  but  its  tendency  to 
leak  in  transportation  and  to  filter  through  crevices  in  the 
rock  is  very  objectionable,  since  in  a  thin  film  it  is  easily 
exploded  by  impact  and  especially  so  by  friction.  Cans 
containing  it  have  been  exploded  by  twisting  the  cork.  The 
granular  form  is  advantageous  on  account  of  the  ease  with 
which  it  may  be  loaded  into  bottle  shaped  cavities,  as  in 
hollow  projectiles  and  torpedoes.  Rigid  prisms  form  con- 
venient packages  for  transportation,  but  require  cavities 
of  a  special  form  to  develop  the  best  results. 
Cold. 

When  in  a  liquid  or  plastic  form,  the  high  explosives  have 
their  sensitiveness  much  impaired  by  freezing.  This  occurs 
at  a  little  above  0°. 

The  force  and  sensitiveness  of  loose  dynamite  are  not  im- 
paired by  its  freezing. 

Heat. 

In  such  cases  thawing  is  dangerous  unless  very  gradually 
performed,  as  by  the  heat  of  the  body,  of  manure,  or  of  luke- 
warm water. 

The  nitro-glycerine  in  frozen  dynamite  of  the  solid  form 
tends  to  exude  on  thawing. 

The  sensitiveness   of  an   explosive  increases    with    its 
temperature. 
Water. 

Nitro-glycerine  and  gun-cotton  are  insoluble.  Water  tends 
to  displace  the  nitro-glycerine  from  dynamite' which  has  been 


XTV. — HIGH    EXPLOSIVES. 


compressed;  but,  strangely,  has  no  such  effect  upon  that 
which  is  loosely  granular.  For  this  reason  sub-aqueous 
torpedoes  are  charged  with  loose  dynamite. 

Owing  to  its  greater  density  the  displaced  nitro-glycerine 
settles  to  the  bottom  of  the  vessel  containing  the  dynamite, 
whence  it  may  exude  and  lead  to  the  consequences  noted 
above. 

When  dynamite  or  gun-cotton  is  wet,  it  ignites  with  great 
difficulty  but  may  be  detonated  by  a  powerful  primer.    Any 
soluble  addition  is  of  course  removed  by  water. 
TTse. 

Except  gun-cotton  and  the  picrates,  all  the  high  explosives 
have  so  far  been  employed  only  for  mining  and  demolition, 
and  to  a  limited  extent  in  pyrotechny. 

Efforts  are  constantly  making  to  adapt  them  to  the  burst- 
ing charges  of  hollow  projectiles,  by  affecting  either  their 
condition,  the  construction  of  the  projectile,  or  the  source 
of  energy  by  which  it  is  thrown. 

Such  attempts  have  not  yet  (1888)  wholly  passed  beyond 
the  stage  of  experiment  and,  though  occasionally  successful, 
have  yet  to  endure  the  test  of  long  continued  firing.  In 
many  cases  it  appears  that  failure  comes  less  from  explosion 
under  the  initial  shock  than  from  the  friction  due  to  the 
rotation  of  the  projectile.  If  the  initial  shock  or  acceleration 
be  diminished,  flatness  of  trajectory  is  sacrificed  or  the  gun 
is  made  inconveniently  long;  if  the  rotation  of  the  projectile 
is  abandoned,  inaccuracy  results. 

The  sensitiveness  of  the  explosive  tends  to  cause  a  prema- 
ture explosion  on  impact  against  armor  and  its  force  tends 
to  pulverize  the  envelope  into  ineffective  fragments. 

The  sphere  of  such  explosives  appears  to  be  confined  to 
the  ordinary  sub-aqueous  mines  or  to  their  employment  in 
aerial  torpedoes,  exploding  under  water  in  the  vicinity  of  a 
vessel,  as  in  the  Zalinski  system;  or  against  earth  works  as 


XIV. — HIGH    EXPLOSIVES. 


in  the  new  gun-cotton  shell  now  employed  in  Germany. 
This  projectile  has  been  fired  with  charges  as  great  as 
110  lbs.  Captain  Zalinski  has  fired  a  mixed  charge  of  high 
explosives  weighing  500  pounds  to  a  distance  of  one  mile. 

Some  of  the  high  explosives,  notably  the  gun-cotton  class, 
have  been  used  for  fire  arms,  principally  in  fowling  pieces, 
for  which  the  reasons  assigned,  Chap.  XI,  page  18,  particu- 
larly adapt  them.  The  absence  of  smoke  is  a  considerable 
advantage.  They  have  even  been  employed  by  the  Austrians 
for  field  pieces. 

The  uncertainty  as  to  the  order  of  the  explosion  resulting 
from  accidental  variations  in  the  value  of  A ,  has  caused  their 
use  in  cannon  to  be  abandoned.  For  the  former  purpose  it 
is  still  unfortunately  common. 

GUN  COTTON. 
Forms. 

This  occurs  in  three  forms;  viz.: 

1.  In  the  flocculent  or  pulverulent  form,  made  from  cotton 
wool  as  indicated  in  the  chemistry. 

2.  Prepared  from  the  first  form  by  pulping  and  com- 
pression to  a  density  a  little  greater  than  that  of  water. 

3.  In  grains,  made  by  disintegrating  the  second  form 
above. 

Condition. 

The  first  form  is  always  used  dry  and  is  employed  only  in 
pyrotechny.    The  other  two  are  used  either  wet  or  dry,  and 
when  wet,  are  sometimes  protected  by  a  water-proof  coating 
to  retard  evaporation. 
Firing. 

Dry  gun-cotton  ignites  at  a  lower  temperature  than  any 
other  of  the  common  explosives.  Its  combustion  may  be 
retarded  by  compression  and  the  addition  of  a  gum. 

When  it  contains  from  20  to  30  per  cent  of  water,  it  can- 


XIV.— HIGH   EXPLOSIVES. 


not  be  ignited  until  the  water  has  been  evaporated  by  the 
flame.     One  ton  of  loose  wet  gun-cotton  has  been  burned 
with  safety  in  a  bon-fire 
Detonation. 

When  wet  and  compressed,  it  may  be  detonated  by  using 
a  sufficiently  large  primer  of  dry  gun-cotton.  Its  incorpo- 
ration in  a  dry  state  with  paraffine  is  said  to  yield  the  same 
results  as  to  safety  as  when  it  is  wet,  without  diminishing 
its  sensitiveness  to  detonation.  This  avoids  the  difficulty 
of  preventing  evaporation. 
Reaction. 

This  varies  with  the  value  of  A  and  with  other  conditions, 
but  may  be  represented  by  the  following  formula, 
2QH7(N02)3  05=70H2H-3C02  +  9CO  +  6N. 

To  increase  its  potential  a  nitrate  or  chlorate  is  often 
added,  the  latter  being  the  more  energetic. 

Gun-cotton  mixed  with  one  third  its  weight  of  a  nitrate 
forms  Tonite,  an   explosive  much  used  in  the  Californian 
mines. 
Advantages. 

Compared  with  gunpowder,  its  manufacture  is  less  danger- 
ous and  the  apparatus  can  easily  be  improvised  from  the 
paper-mills. 

Since  it  forms  no  dust  and  can  be  kept  wet,  it  is  safe  in 
transportation  and  in  store. 

In  mining,  as  in  fire  arms,  it  yields  no  solid  products,  and 
in  sub-marine  mining  it  can  be  used  under  water;  having 
even  been  detonated  in  a  net. 
Disadvantages. 

Besides  those  which  relate  to  its  sensitiveness  and  vio- 
lence, the  principal  objection  to  its  employment  in  artillery 
applies  to  the  absence  of  smoke  which  serves  to  mark  the 
bursting  point  of  a  distant  shell. 


10  XIV. — HIGH   EXPLOSIVES. 


MANUFACTURE    OF    GUN-COTTON, 

rormer  Method. 

Gun-cotton,  like  nitro-glycerine,  was  discovered  about 
1846.  It  was  first  made  by  dipping  cotton  wool  into  mixed 
sulphuric  and  nitric  acid  and  washing  thoroughly  the  gun- 
cotton  wool  so  formed.  But  it  was  found  to  be  impossible 
to  remove  the  free  acids  from  the  tortuous  capillary  tubes 
of  which  cotton  wool  is  composed,  and  the  resulting  product 
was  dangerous  in  store. 
Abel's  Method. 

The  tim?  of  manufacture  has  been  much  reduced  and  the 
quality  of  the  product  improved  by  the  following  method. 

Instead  of  using  raw  cotton,  often  containing  impurities 
which  are  liable  to  cause  spontaneous  decomposition,  cotton 
waste  is  employed.     This  has  been  previously   spun  mto 
yarn  for  cloth  and  is  therefore  mechanically  clean. 
Preliminary  Operations. 

Its  conversion  into  gun-cotton  follows  the  method  previ- 
ously taught,  the  essential  points  being: — 

1.  To  prevent  the  continued  action  of  dilute  acids  and 
the  consequent  formation  of  di-nitro-cellulose  (Collodion 
cotton),  by  removing  the  cotton  after  its  first  immersion 
to  a  fresh  mixture  of  acids  in  which  it  is  soaked  for  several 
hours.  After  each  immersion  the  excess  of  acid  is  removed 
by  wringing. 

3.  To  prevent  an  undue  rise  in  temperature,  by  making 
the  first  immersion  in  small  quantities  at  a  time,  and  sur- 
rounding the  vessels  containing  the  cotton  with  running 
water. 

3.  To  prevent  the  access  of  water  to  these  contents.     A 
drop  of  sweat  may  cause  the  acid  cotton  to  ignite. 
Final  Operations. 

After  the  final  wringing,  it  is  washed  by  plunging  small 
quantities  of  the  cotton  into  large  quantities  of  water. 


XIV.    -HIGH    EXPLOSIVES.  11 

The  cotton  is  then  reduced  to  a  pulp  by  the  rotary  knives 
of  the  rag  engine  used  in  paper  making.  These  operate 
under  water. 

Being  now  in  short  tubes,  the  washing  can  be  thoroughly 
performed  by  means  of  the  paper  maker's  poacher.  This  is 
a  vertical  water  wheel  working  on  one  side  of  an  oblong 
trough  through  which  a  longitudinal  partition  extends 
nearly  from  end  to  end. 

After  a  protracted  washing  in  the  poacher,  the  free  acids 
still  remaining  are  neutralized  by  some  alkali;  this  having 
been  washed  out,  the  pulp  is,  after  draining,  ready  for  the 
hydraulic  press. 

After  pressing  the  cylinders  they  are  carefully  and  slowly 
dried;  or,  they  may  be  kept  wet  as  previously  stated. 

A  similar  product  has  been  made  from  bran  or  straw,  and 
is  known  djs,  fulmi-bran^  etc. 

NITRO-GLYCERINE. 

Manufacture. 

The  preparation  of  this  explosive  has  been  sufficiently 
described  in  the  course  of  chemistry  The  principal  points 
to  be  observed  are: —  m 

1.  To  prevent  a  rise  in  temperature  by  pouring  the 
glycerine  slowly  into  the  mixed  acids,  and  to  preserve  a  low 
temperature  by  a  jacket  of  running  water  and  by  agitating 
the  mixture  by  a  current  of  air. 

2.  To  wash  the  product  thoroughly  with  cold  water  and 
finally  with  an  alkaline  solution.  The  addition  of  cold  water 
precipitates  that  portion  of  the  nitro-glycerine  which  remains 
suspended  in  the  heavy  acid  liquid. 

Too  much  importance  cannot  be  attached  to  the  entire  removal 
of  free  acid.  The  detection  of  free  acid  constitutes  one  of 
the  most  important  tests  of  this  product. 


12  XIV. — HIGH    EXPLOSIVES. 

When  first  made,  it  is  white  and  opaque;  \t  soon  assumes 
an  oily  appearance  which,  if  well  made,  it  retains.  Its  density 
is  about  1.6. 

Reaction. 

The  explosion  of  nitro-glycerine  gives  the  following 
reaction, 

2C3H5(NO,)3  03=6CO,+  6N4-0  +  5  0H«. 

Following  a  general  law,  since  its  composition  furnishes 
an  excess  of  oxygen,  the  reaction  is  sensibly  constant  and  is 
found  to  agree  with  that  deduced  on  theoretical  grounds. 
In  this  respect  it  differs  from  most  of  the  explosives. 

Special  Properties. 

As  ordinarily  used,  this  is  the  most  powerful  of  the  ex- 
plosives, excelling  both  in  potential  and  force. 

It  was  originally  thought  to  be  perfectly  safe  when  frozen; 
but  it  has  since  been  found  that,  when  in  this  condition,  it 
can  be  exploded  by  a  powerful  shock  if  concentrated  upon 
a  mass  sufficiently  small. 

DERIVATIVES  OF  NITRO-GLYCERINE. 

Owing  to  the  dangerous  properties  of  liquid  nitro- 
glycerine, it  is  no  longer  employed  except  with  an  absorbent 
dase  or  dope  which  will  prevent  its  exudation. 

The  absorbents  are  of  two  kinds: — 

I.  Those  which  are  chemically  inactive,  such  as  kiesel- 
guhr  (also  known  as  "  tripoli "  and  "  electro-silicon  "),  mica- 
ceous scales,  and,  for  its  alkaline  properties,  magnesium 
carbonate. 

II.  Those  which  are  chemically  active. 

These  derivatives  have  a  density  of  about  1.6.  They  are 
usually  plastic,  which  gives  them  great  practical  utility. 


XIV. — HIGH    EXPLOSIVES.  13 


I.    MECHANICAL   ABSORBENTS. 

Dynamites.     Giant  Powder. 

Of  these  absorbents  the  best  is  kieselgiihr.  This  consists 
of  microscopic  shells,  the  cavities  in  which  retain  the  liquid 
and  protect  it  from  ordinary  shock.  Kieselgiihr  has  remark- 
able properties  as  an  absorbent;  it  can  take  up  three  times 
its  weight  of  nitro-glycerine  without  exudation,  even  when 
under  considerable  pressure. 

Different  grades  of  dynamite  are  made  depending  upon 
the  proportion  of  nitro-glycerine  which  they  contain.  The 
highest  is  called  No.  1. 

Owing  to  the  knowledge  of  the  properties  of  this  explosive, 
gained  by  the  torpedo  service  and  by  private  industry,  it 
may  be  called  the  standard  high  explosive  of  the  United 
States.     For  torpedoes  its  merits  consist  in: — 

1.  Its  force. 

2.  Its  permanency  under  the  varied  conditions  and 
accidents  of  service. 

3.  Its  safety  and  convenience  in  loading. 

4.  The  readiness  with  which  it  may  be  procured  in  the 
market. 

This  was  true  in  1881.    Since  then  several  explosives  have 
been  invented  which  threaten  its  supremacy, 
Preservation. 

Although  used  for  special  purposes  in  the  granular  form, 
in  which  it  resembles  brown  sugar,  it  is  generally  put  up 
compressed  in  cylinders  wrapped  tightly  with  paraffined 
paper.  These  are  packed  in  sawdust  in  wooden  boxes, 
preferably  made  light,  without  metallic  parts  and  coated  in- 
side with  a  water-proof  varnish. 

When  received,  the  boxes  should  be  partly  opened  to 
facilitate  the  discovery  of  the  nitrous  fumes  that  accompany 
the  process  of  spontaneous  decomposition.    Their  contents 


14  XIV. — HIGH   EXPLOSIVES. 

should  be  tested  for  exudation  and  acidity,  and  should  be 
carefully  kept  from  water, 

•    II.    CHEMICAL    ABSORBENTS. 

Properties. 

Absorbents  of  this  class  reduce  the  quantity  of  nitro- 
glycerine required  to  produce  a  given  effect  and  so  cheapen 
the  product. 

Their  judicious  selection  adds  greatly  to  the  energy 
developed  by  the  nitro-glycerine  alone,  so  that  the  economic 
value  of  the  explosive  may  increase  more  rapidly  than  does 
'its  percentage  of  nitro-glycerine. 

For  sub-aqueous  explosions  it  appears  that  with  any  par- 
ticular base  there  is  an  economic  gain  in  increasing  the  per- 
centage of  nitro-glycerine  up  to  a  certain  point,  but  that 
beyond  that  point  the  advantage  ceases.  There  appears  to 
be  a  decided  advantage  in  gelatinizing  the  nitro-glycerine 
before  its  absorption. 

See  Forcite  and  Explosive  Gelatine, /<?j/. 

Classification. 

The  chemical  absorbents  may  be  conveniently  divided 
into  two  general  groups,  according  as  they  are  simply  com- 
bustible, or  in  themselves  high  explosives. 

Class  I.     A  combustible  dope. 

When  finely  ground  cellulose  is  treated  with  super-heated 
steam,  it  is  converted  into  a  jelly  capable  of  absorbing  19 
times  its  weight  of  nitro-glycerine.  With  or  without  the 
addition  of  nitre,  it  forms  Foi^cite^  a  most  powerful  explosive. 

Gunpowder,  preferably  made  after  Col.  Wiener's  method, 
Chap.  IV,  may  be  coated  with  nitro-glycerine,  the  detonation 
of  which  detonates  powder,  Chap.  XI,  This  foruas  the 
Jtidson  powder. 


Class  II,     A  high  explosive  as  a  dope. 

The  most  famous  is  known  as  Explosive  Gelatine.  This 
consists  of  about  93  per  cent  of  nitro-glycerine  with  7  per 
cent  of  collodion  gun-cotton  (di-nitro-cellulose).  The 
addition  of  3  or  4  per  cent  of  camphor  greatly  diminishes 
its  sensitiveness  and  adapts  it  particularly  for  warfare. 

It  is  generally  a  transparent  jelly,  but  often  becomes  hard 
and  opaque.  The  fulmi-bran,  page  11,  may  replace  the 
collodion  cotton. 

Although  found  by  General  Abbott  to  be  stronger  than 
nitro-glycerine,  it  is  much  safer,  particularly  against  shock. 
It  has  been  found  to  burn  freely  without  explosion,  even 
when  confined,  and  to  resist  perfectly  the  action  of  water. 

It  requires  an  initial  primer  for  its  detonation  and  the 
weight  of  the  primer  required  increases  as  its  sensitiveness 
diminishes. 

When  the  collodion  cotton  is  not  thoroughly  purified,  this 
explosive  tends  to  decompose  spontaneously.  Otherwise  it 
is  quite  stable. 

New  smokeless  powder. 

By  reversing  the  proportions  of  nitro-glycerine,  and  col- 
lodion used  in  explosive  gelatine,  and  retaining  the  camphor, 
the  compound  becomes  plastic  when  heated.  It  may  then 
be  pressed  into  sheets  or  drawn  into  wires  or  rods  which,  on 
cooling,  become  horn-like,  like  the  celluloid  of  commerce. 

The  reduction  of  w  and  the  increase  of  \i  are  reported  to 
give  in  the  6  in.  Rifle  a  value  oi  %•=.  100  -f-.  Its  tactical 
advantages  adapt  it  particularly  to  rapid  firing  arms  of  small 
caliber.  The  special  difficulties  to  be  overcome  refer  to  the 
volatiUty  of  the  camphor  and  to  the  erosion  of  the  bore  re- 
sulting from  the  heat  of  the  explosion.    See  Chap.  IX,  Notes. 

NITRO-BENZINE  OR  -BENZOLE. 

The  preparation  of  this  resembles  that  of  nitro-glycerine, 


16  XIV. HIGH    EXPLOSIVES. 


the  mono-  (liquid),  and  di-,  and  tri-nitro  benzines,  (crystal- 
line) being  formed.     (Bloxam,  Art.  325.) 

These  substitution  products  are  in  themselves  inexplosive, 
and  show  by  their  composition,  C^  H^(N02)g_j,  ^^^  necessity 
for  the  addition  of  an  oxydizing  agent. 

Rack-a-Rock  is  made  at  the  time  of  its  employment  by 
saturating  K  CIO3  with  crude  mono-nitro-benzine,  or  even 
with  the  "dead  oil"  from  the  gas  works  which  has  been 
diluted  with  CSg  containing  a  small  proportion  of  sulphur. 
By  exposure  to  the  air  the  CSg  evaporates,  leaving  the  finely 
divided  sulphur  on  the  salt  but  protected  by  the  lubricating 
property  of  the  oil  or  nitro-benzine  against  explosion  by 
friction. 

When  the  dope  is  finely  ground  and  the  charge  exploded 
by  a  powerful  primer  it  is  found  to  be  nearly  as  powerful 
as  dynamite  No.  1. 

This  is  the  only  chlorate  mixture  which  has  been  found 
safe  in  practice. 

Helhofite^  as  used  in  Germany  for  armor  piercing  pro- 
jectiles, is  another  of  the  Sprengel  Safety  Mixtures  pre- 
pared as  wanted  by  dissolving  di-nitro-benzine  in  nitric  acid. 

Bellite  (La.tin:  Bel/um — War),  is  a  recent  Swedish  explosive 
made  of  about  -J  tri-nitro-benzine  and  |  ammpnium  nitrate, 
incorporated  together. 

This  is  distinguished  by  its  great  safety  under  all  con- 
ditions and  by  its  greater  potential  as  compared  with 
dynamite, 

Only  dampness  affects  it.  It  is  almost  incombustible, 
smouldering  only  by  the  continued  application  of  flame. 
It  is  so  insensitive  to  shock  that  the  detonation  of  itself  upon 
a  box  filled  with  the  explosive,  or  the  explosion  of  gunpowder 
in  its  midst  fails  to  explode  it.  A  wad  of  it  has  been  fired 
from  a  fowling  piece  against  a  target  without  injury  to  either. 
It   gives  no   injurious   gases,  nor   flame,  which   properties. 


XIV. — HIGH    EXPLOSIVES.  .    17 

together  with  its  high  potential,  particularly  adapt  it  for  the 
coal  miner.  It  is  also  cheap  and  indifferent  to  variations  in 
temperature. 

Tamping  is  necessary  to  develop  its  full  effect,  even  when 
detonated ;  but  when  tamped  and  detonated,  it  is  about  33 
per  cent  stronger  than  dynamite. 

The  crystaline  form  of  the  two  ingredients  of  Bellite 
would  appear  to  insure  its  stability  in  store  and  to  make  of 
it  one  of  the  best  high  explosives  where  potential  is  required, 
as  in  torpedo  shells.  For  sub-aqueous  mining,  dynamite  is 
probably  better  suited. 

PICRIC  ACID  (TRI-NITRO-PHENOL). 

This  is  made  by  the  action  of  nitric  acid  on  carbolic  acid 
(phenol).  It  occurs  in  slightly  soluble  plates  of  a  bright 
yellow  and  is  much  used  in  dyeing.  Unconfined,  it  will  not 
explode  by  heat,  but  may  be  detonated. 

When  mixed  with  gun  cotton  dissolved  in  ether,  it  is  said 
to  form  the  new  French  explosive,  Melinite. 

Emmensite  is  a  recent  American  explosive,  prepared  from 
crystallized  Emmens  acid  and  a  nitrate.  The  acid  results 
from  the  solution  of  picric  in  nitric  acid. 

The  claims  made  for  this  explosive  resemble  those  noted 
under  the  description  of  Bellite.  It  is  (1891)  under  trial  in 
the  United  States. 

THE   PICRATES. 

The  potassium  and  ammonium  salts  are  the  only  ones 
employed. 

The  former  with  the  addition  of  nitre  and  charcoal  forms 
Designolle's  powder.  This  was  found  too  dangerous  for 
use,  as  it  tends  to  detonate  on  ignition. 

The  ammonium  salt  is  less  sensitive  to  shock  and  burns 
in  the  air  like  resin.     With  the  addition  of  a  nearly  equal 


18  XIV. HIGH    EXPLOSIVES. 

part  of  nitre  and  prepared  like  ordinary  gunpowder,  it  forms 
the  powder  of  Briigere.  In  small  arms,  a  charge  less  than 
one  half  the  charge  of  ordinary  gunpowder  suffices  to  pro- 
duce the  same  effects.  This  is  of  importance  since  it  enables 
the  size  and  weight  of  the  cartridge  used  in  magazine  rifles 
to  be  greatly  reduced. 

The  powder  yields  no  smoke  or  fouhng  but  is  hygroscopic. 

It  is  believed  that  the  new  powder  used  in  the  French 
Lebel  rifle  is  a  variety  of  Brugere  powder. 

THE  FULMINATES. 

The  mercuric  salt  is  the  only  one  of  practical  value.  Its 
efficiency  depends  rather  upon  its  force  and  the  nature  of 
its  product  than  upon  the  heat  evolved  by  its  decomposition. 

This  follows  from  the  reaction, 

C2HgN2  0a=:2CO  +  Hg  +  2N. 

Its  force  is  said  to  be  nearly  10  times  that  of  gunpowder. 

When  dry  it  is  easily  detonated  by  shock,  friction,  a  tem- 
perature of  about  200°,  or  by  the  strong  acids. 

Certhelot  finds  that  even  so  stable  a  gas  as  nitric  oxide 
is  dissociated  by  the  detonation  of  mercuric  fulminate. 
While  for  detonation  it  is  preferably  used  pure,  for  igniting 
the  charges  of  fire  arms  it  is  mixed  with  an  oxydizing  agent 
and  often  a  combustible,  in  order  to  increase  the  length  of 
the  flame.  Powdered  glass  's  also  added  v/hen  the  salt  is 
expiod'^d  by  percussion. 

Its  safety  in  manufacture  depends  upon  its  absolute  in- 
explosiveness  when  wet.  If  placed  upon  a  metallic  surface, 
it  tends  to  decompose;  hence,  percussion  caps  are  varnished 
before  they  are  primed. 

Under  no  circumstances  should  the  fulminate  be  carried  or 
stored  near  any  of  the  high  explosives. 


XIV. HIGH    EXPLOSIVES.  19 


CHLORATE  MIXTURES. 

Since  their  discovery,  a  century  ago,  frequent  efforts  have 
been  made  to  utilize  the  chlorate  mixtures  in  mining  and  as 
a  substitute  for  gunpowder.  Their  extreme  sensitiveness 
to  friction  has  almost  uniformly  caused  their  employment 
for  such  purposes  to  result  in  disaster. 

Mixed  with  Sbg  S3,  the  potassium  chlorate  forms  the  friction 
composition  used  in  cannon  primers.  It  is  also  employed  in 
pyrotechny  to  compensate  for  the  cooling  effect  of  sub- 
stances employed  to  give  color  and  brilliancy  to  the  flame. 

GENERAL  REMARKS  ON  THE  EMPLOYMENT  OF 
THE  HIGH  EXPLOSIVES. 

In  Guns. 

Their  employment  has  always  failed,  except  for  small  arms 
and  as  noted  page  8. 

For  Bursting  Charges  of  Hollow  Projectiles.* 

Explosive  gelatine  has  been  occasionally  fired  without 
premature  explosion,  by  the  use  of  diaphragms  within  the 
shell.  See  also  gun-cotton,  and  the  experiments  with  the 
Zalinslii  gun  before  noted. 

For  Demolition  of  "Walls,  etc. 

Unless  the  wall  is  very  strong,  the  best  results  in  breach- 
ing appear  to  follow  the  detonation  of  the  explosive  at  the 
base  of  the  wall  and  at  a  few  inches  distant.  This  distrib- 
utes the  effect,  and  racks  and  fissures  the  wall  so  as  to  facili- 
tate its  destruction  by  hand. 

Exploded  in  immediate  contact,  a  smaller  hole  is  said  to 
be  made  and  the  energy  to  be  expended  in  giving  motion 

*  The  premature  explosion  of  such  bursting  charges  by  the  shock  of 
discharge  is  often  attributed  to  the  sensitiveness  of  the  fulminate  neces- 
sarily used  in  the  detonating  fuze. 


20  XIV. — HIGH    EXPLOSIVES. 

to  but  few  fragments.    About  10  lbs.  of  dynamite  will  open 
a  practicable  breach  in  a  two  foot  stone  wall.     Tamping 
would  reduce  the  size  of  the  charge  required. 
Houses,  Palisades,  etc. 

About  5  lbs.  of  dynamite  will  wreck  a  small  stone  dwelling 
if  exploded  near  its  center,  since  it  tends  to  overthrow  all 
the  walls  instead  of  blowing  out  through  the  nearest  one. 
The  same  quantity  suffices  for  a  linear  yard  of  ordinary 
palisading.  A  pound  of  dynamite  will  shatter  a  12  inch 
bridge  timber.* 
Disabling  Cannon. 

When  time  permits,  bring  the  gun  as  nearly  vertical  as 
possible;  fill  it  with  water,  plug  it,  and  explode  simultane- 
ously two  one  pound  charges  of  gun-cotton,  one  at  the 
bottom  of  the  bore  and  one  in  the  chase.  When  time  is 
scant,  insert  a  shot  within  the  bore,  and  place  on  top  of  the 
chase,  between  the  shot  and  the  muzzle,  two  pounds  of  gun- 
cotton,  laying  over  it  a  filled  sand  bag  or  a  sod.  Such  charges 
are  said  in  the  English  Manual  to  suffice  for  the  lighter 
natures  of  sea  coast  guns. 

It  is  found  to  be  more  advantageous  to  attack  the  cannon 
themselves,  than  to  waste  time  and  explosive  material  on 
their  carriao:es. 


♦These  directions  are  intended  to  apply  only  to  hasty  operations. 
When  time  permits,  the  best  results  will  follow  from  placing  the  charge 
under  or  within  the  structure  to  be  demolishedo  The  quantities  are 
approximate. 


XV. — M£T  ALLURG  Y. 


CHAPTER  XV. 
METALLURGY. 

I.  TESTING  MACHINES. 

Necessity. 

The  physical  properties  of  a  metal  may  sometimes  be  in- 
ferred from  a  knowledge  of  its  chemical  composition,  but  so 
many  other  causes  may  contribute  to  modify  these  properties 
that  chemical  analysis  should  be  depended  on,  rather  to  indi- 
cate the  existence  of  certain  limiting  or  possible  conditions 
than  to  declare  the  extent  to  which  these  conditions  have 
been  approached.  Thus,  what  a  metal  is  becomes  subordi- 
nate to  what  it  can  do  ;  and  its  proof  is  more  conclusive  than 
even  its  chemical  inspection. 

Requisites. 

A  complete  testing  machine  should  include  means  for  de- 
termining the  varying  strains  under  tensile,  crushing,  trans- 
verse, torsional,  and  shearing  stresses.  But  for  simplicity, 
and  on  account  of  the  comparative  ease  with  which  all  stresses 
can  be  referred  to  that  first  named,  such  machines  are  gen- 
erally of  the  tensile  type. 

Comparisons. 

For  establishing  comparisons  the  stresses  are  usually  meas- 
ured per  unit  of  minimum  area  of  cross  section,  and  the 
strains  per  unit  of  length  between  established  points  on  the 
specimen.  But  if  the  form  and  dimensions  of  the  specimens 
are  constant,  absolute  measures  may  be  compared.  In  the 
following  discussion  stresses  and  strains  will,  unless  otherwise 
stated,  be  taken  per  unit  of  section  and  of  length. 


XV. — metallurCV. 


In  the  United  States  stresses  are  given  in  pounds  per  square 
inch;  in  England  in  tons  of  2240  lbs.  per  square  inch;  in 
France  in  kilogrammes  per  square  centimetre;  in  Russia  and 
Germany  in  atmospheres. 

Form  of  Specimen. 

Since  the  deductions  from  proof  are  conclusive  only  as  to 
the  actual  piece  tested  and  are  inferential  as  to  all  others, 
the  above  precautions  for  the  comparison  of  properties  are 
not  wholly  sufficient.  The  general  •  rule  in  experimental 
comparisons,  of  dealing  with  but  one  variable  at  a  time, 
should  be  followed  by  subjecting  specimens  as  nearly  as 
possible  in  size  and  shape  lik>e  those  to  be  actually  employed 
to  the  same  kind  of  stress  that  they  will  be  called  on  to  sustain. 

But  the  capacity  of  the  machine  rarely  permits  this,  and, 
as  its  strength  limits  the  maximum  cross  section,  the  length 
of  the  specimen  in  units  of  the  corresponding  diameter  should 
be  approximately  proportional  to  that  of  the  finished  piece. 
The  size  of  the  machine  and  the  cost  of  preparing  specimens 
limit  this;  so  that  the  length  of  the  specimen  is  generally 
about  4,  6,  or  8  diameters,  with  a  tendency  to  increase. 

The  specimen  is  held  so  that  its  axis  coincides  with  the 
action  line  of  the  force;  otherwise,  it  will  rupture  in  detail, 
or  tear  across.  This  condition  is  fulfilled  by  making  the 
specimens  truly  cylindrical  with  enlarged  concentric  heads, 
figure  3,  by  which  they  may  be  held  in  the  machine. 

Form  of  Record. 

This  states  the  strains  due  to  certain  stresses.  They  are 
functions  of  each  other,  and  the  relation  may  be  expressed 

e  —f{w), 

in  which  e  represents  the  strain,  or  the  change  of  form  pro- 
duced by  applying  the  stress  w.  The  stress  is  taken  as  the 
independent  variable  since  it  can  be  more  readily  controlled 


XV. — METALLURGY. 


than  the  strain.  Inasmuch  as  conditions  vary  too  much,  and 
are  not  yet  sufficiently  understood  to  enable  the  law  of  this 
function  to  be  analytically  expressed,  that  which  governs  any 
particular  case  may  be  best  determined  empirically: 

1st.  By  forming  successive  orders  of  difference  in  the 
observed  value  of  the  function  for  equal  increments  of  the 
variable  w. 

2d.  By  plotting  a  line  constructed  from  these  co-ordinate 
values.     Such  a  line  is  called  a  strain  diagram. 

3d.  By  constructing  a  strain  diagram  automatically  during 
the  progress  of  the  test. 

The  order  of  preference  is  as  follows: 

The  first  method  when  great  accuracy  is  required  and 
when  a  micrometer  can  be  used. 

The  second  and  third  when  general  comparisons  are  to  be 
made. 

The  second  to  the  third  when  the  expense  of  the  registering 
apparatus  is  objectionable. 

In  general,  rectilinear  strains  can  be  measured  more  accu- 
rately than  they  can  be  registered  by  any  mechanical  apparatus. 

ELASTICITY. 

Elastic  Limits 

In  operating  the  machine  the  stress  is  very  slowly  and  stead- 
ily applied,  either  directly  by  hydraulic  pressure,  or  indirectly 
by  a  screw  acting  in  combination  with  levers.  The  stress  is 
relieved  at  intervals  and  the  specimen  permitted  to  recoil. 

The  difference  between  the  strain  e  and  the  recoil  r  is  the 
set  s,  ov  e  =  r  -\-  s.  The  set  may  diminish  in  time  and  be- 
come the  permanent  set,  but  the  first  temporary  set  is  that 
generally  recorded.  Sets  probably  occur  under  all  stresses, 
but  may  be  too  small  for  measu^-ement.  This  may  be  illus- 
trated by  the  curves,  figure  1,  which  are  very  much  exagger- 
ated. 

Let  00\  00"  represent  certain  stresses  resulting  in  strains 
O'p' ,  0"p'\  etc.     Each  of  these  strains  is  by  definition  com- 


XV. — METALLURGY. 


posed  of  the  recoil  r  —  r'p'  and  the  set  s  =  O'r' ,  etc. 
Starting  from  0,  as  the  stresses  increase  the  recoils  and  sets 
both  increase,  but  the  sets  less  rapidly  than  the  recoils. 

After  a  certain  stress,  Z,  the  line  of  sets  becomes  nearly 
parallel*  to  that  of  strains,  so  that  for  a  given  increment  of 
stress  the  increments  of  strain  and  set  are  nearly  equal.  The 
stress  corresponding  to  L  is  the  superior  limit  of  the  stresses 
for  which  the  sets  increase  less  rapidly  than  the  recoils,  and 
the  inferior  limit  of  those  for  which  the  sets  increase  more 
rapidly  than  the  recoils.  This  stress  is  called  the  Elastic 
Limit. 

Since  below  the  elastic  limit  the  sets  are  relatively  small, 
and  above  it  the  sets  are  relatively  large,  when  compared 
with  the  recoils,  it  may  be  defined  as  the  limit  of  the  stresses 
within  which  sets  may  be  neglected  and  beyond  which  recoils  may 
he  neglected ;  or  the  limit  separating  the  consideration  of  the 
elasticity  of  the  metal  from  that  of  its  ductility. 

It  may  be  determined — 

I.  By  finding  the  stress  corresponding  to  the  first  significant 
term  of  the  second  order  of  difi"erences  of  strains  or  sets. 

II.  By  inspection  of  a  diagram  such  as  represented  in  fig- 
ure 13. 

Coefficient  of  Elasticity. 

If  the  strains  below  the  elastic  limit  be  considered  directly 
proportional  to  the  stresses,  this  portion  of  the  line  will  be 
straight,  and  the  tangent  of  the  angle  included  between  it  and 
the  axis  of  E  will  be  proportional  to  the  reciprocal  of  the 
rate  at  which  the  specimen  submits  to  (i.e.,  directly  to  the 
rate  at  which  it  resists)  the  stress.  This  is  called  the  coeffi- 
cient of  elasticity,  or 

^  _  r^  _  ^      ^     /Wheeler,  \ 
^  ~  Z  ^  7  '  V  Eq.  1.  y 

*  As  a  rule,  the  recoils  increase  gradually  throughout. 


XV.— -METALLURGY. 


Elastic  Work,  etc. 

The  area  bounded  by  the  diagram,  the  axis  of  E,  and  a 
line  drawn  through  any  point  of  this  axis  parallel  to  the  axis 
of  PFis  evidently  proportional  to  the  work  done  by  the  corre- 
sponding stress. 

For  a  given  stress  O  O'",  the  area,  O  e  r"',  is  proportional 
to  the  work  of  permanent  deformation  corresponding  to  the 
stress  O  O'".  Similarly  the  difference  between  the  areas 
0^'/'"and  O^r'"  is  proportional  to  the  work  of  restitution, 
or  the  elastic  work,  following  the  same  stress.  The  term 
Elastic  Work,  as  a  measure  of  this  elastic  property,  also 
known  as  toughness,  is  properly  applied  only  to  the  area 
under  the  diagram  at  the  elastic  limit. 

The  total  area  under  the  diagram  up  to  the  point  of  rup- 
ture is  proportional  to  the  potential  work  of  deformation.  While 
for  mechanical  units,  such  as  posts,  beams,  levers,  chains,  this 
property  is  valuable;  in  the  more  complex  structures  required 
by  the  principle  of  the  independence  of  function,  such  as 
wheels,  trusses,  and  built-up  guns,  the  elastic  work,  which 
comprises  in  its  measure  both  the  elastic  limit  and  the  coeffi- 
cient of  elasticity,  is  much  more  important. 

In  such  structures  the  permanent  change  of  form  of  one  of 
the  units  may  derange  the  rest;  and  generally  the  elastic 
work  may  be  counted  on  repeatedly,  while  the  work  of  per- 
manent deformation  can  be  utilized  but  once. 


FORMS   OF    TESTING   MACHINES. 

Tensile. 

This  is  the  form  most  generally  used  and  upon  the  indica- 
tions of  which  modern  gun  construction  is  based. 

The  sketch,  figure  2,  shows  a  simple  apparatus  extempo- 
rized for  testing  the  sheet  metal  from  which  small-arm  car- 
tridges are  made.  The  strains  were  taken  from  the  punch- 
maVks  a,b,  and  plotted. 

For  testing  the  metal  of  which  cannon  are  made,  a  form  of 


XV — METALLURGY. 


tensile  machine  recently  devised  in  England  consists  of  a 
hard  steel  cone,  which  by  a  blow  from  a  falling  weight  is 
driven  through  a  ring  cut  concentrically  from  one  of  the 
short  cylinders  composing  the  gun. 

Transverse. 

The  simplest  of  all  is  for  transverse  stress.  The  specimen 
is  placed  on  rollers  kept  at  a  constant  distance  apart.  One 
objection  to  transverse  machines  is  the  difficulty  of  separating 
the  tensile  from  compressive  strain. 

A  valuable  modification  of  this  form  of  machine  is  that 
which  tests  the  capacity  of  the  metal  to  endure  extreme  bend- 
ing, even  to  the  extent  of  working  its  ends  back  and  forth  as 
long  as  the  tenacity  of  the  specimen  permits.  The  bending 
angle  thus  determined  is  one  of  the  readiest  and  best  tests  for 
ductile  material. 

Torsional. 

Although  a  torsional  strain  is  even  more  complex  than  the 
transverse,  yet,  owing  to  the  ease  with  which  the  power 
of  the  lever  may  be  increased;  to  the  simplicity,  compact- 
ness, cheapness  and  rapidity  of  operation  of  machines  of  this 
class;  and  to  the  ease  with  which  the  relative  rotary  motion  of 
the  parts  may  be  made  to  record  the  circumstances  of  the 
test,  this  method  is  very  valuable  where  great  accuracy  is  not 
required,  nor  variation  in  the  form  of  the  specimens  expected. 

For  the  machine  used  in  this  department  of  instruction,  the 
specimens  are  of  the  standard  size  shown  in  figure  3.  This 
requires  direct  comparison  of  results. 

Thurston's  autographic  torsional  testing  machine,     fig- 
ures 4,  5^  G,  1,  8. 

Description. 

Two  similar  wrenches  with  rectangular  jaws,  facing  each 
other,  are  carried  by  the  A  shaped  frames  shown  in  figure  4, 
and  revolve  independently  about  axes  which  are  in  the  same 


XV. — METALLURGY. 


Straight  line.  The  wrenches  are  not  connected  except  by  the 
interposition  of  the  specimen,  which  is  supported  axially  by 
the  conical  points  shown,  and  kept  by  folding  wedges  from 
revolving  in  the  jaws.  The'  arm  B  of  one  wrench  carries  a 
weight  W  at  its  lower  end.  The  other  wrench  is  revolved  by 
a  worm  gear,  P. 

To  the  frame  A  is  secured  a  guide  curve  G,  of  such  form 
that  its  ordinates  are  proportional  to  the  successive  torsional 
moments  exerted  by  B  during  its  revolution. 

The  pencil-holder/^  is  carried  on  the  arm  B,  to  which  it 
is  pivoted  at  a  and  b  so  as  to  oscillate  in  a  plane  perpendicu- 
lar to  that  in  which  B  rotates.  A  spring,  sp^  keeps  the  pen- 
cil-holder in  contact  with  the  guide  curve. 

Operation. 

As  the  worm  gear  revolves  it  tends  to  revolved  and  to  raise 
PTby  means  of  the  specimen  -S". 

As  B  revolves,  the  roller  r  rides  on  the  edge  of  G  so  that 
the  pencil  is  displaced  laterally  in  a  plane  perpendicular  to 
that  of  its  rotation;  the  object  being  to  establish  as  follows  a 
system  of  rectangular  co-ordinate  axes  of  stresses  and  strains, 
to  which  the  position  of  the  pencil  may  be  referred: 

I.  To  make  the  lateral  displacement  of  the  pencil  propor- 
tional to  the  stress,  W.  Since  PTis  proportional  to  the  mo- 
ment of  ^,  which,  since  the  weight  of  B  is  constant,  is  pro- 
portional to  the  sine  of  the  vertical  angle  0,  figure  7,  the 
edge  of  G  is  so  formed  that  when  B  is  rotated,  the  pencil 
will  trace  upon  the  cylinder  D  a  curve  the  equation  of  which 
when  developed  on  a  plane  surface  is  _y  =  ^  sin  0.  In 
this  equation  J/  is  the  variable  ordinate  of  the  curve  measured 
along  that  rectilinear  element  of  D  upon  which  the  pencil 
rests  when  the  inclination  of  ^  =  0,  and  <2  is  a  coefficient 
depending  upon  the  maximum  value  of  _y  permitted  by  the 
construction  of  the  machine. 

II.  To  make  the  peripheral    displacement   of  the    pencil 


XV. — METALLURGY. 


proportional  to  the  strain,  E.  Calling  ;t:  the  developed  path  of 
the  pencil  along  a  circular  element  of  the  cylinder,  we  have 

X  '.  (p>^  \\%TCr  \  360°,  or0  =-— jvand  .'.y=^  as'ml- .x\ 

^  ^      %7tr  -^  \Z7tr     j 

The  circumference  of  the  drum  is  36  inches  and  its  length 
is  5  inches;  therefore,  taking  x  in  inches. 

jj^  =  5  sin  (10 .  x). 

Such  a  curve  having  been  constructed  upon  paper  may  be 
wrapped  around  D,  and  the  edge  of  G  be  adjusted  so  as  to 
make  the  point  of  the  pencil  follow  the  curve  as  B  is  revolved, 
D  being  at  rest. 

The  strain  is  evidently  proportional  to  the  rotation  of  D 
relatively  to  that  of  the  pencil ;  while  the  stress  is  proportional 
to  the  angular  displacement  of  the  pencil.  This  will  be  un- 
derstood by  imagining  lines  traced  by  specimens  which  are 
either  perfectly  extensible  or  perfectly  inextensible.  Such 
lines  are  limits  for  all  natural  specimens  which  will  cause  in- 
termediate lines  to  be  traced  that  will  express  the  relation 
e  ^/{w). 

Form  of  Record. 

The  record  is  made  on  a  piece  of  cross-section  paper  ruled 
in  inches  and  tenths  w^rapped  tightly  around  the  cylindrical 
drum  D. 

The  weight  W  is  so  taken  that  the  maximum  moment 
=  500  lbs. ;  therefore,  since  the  ruling  is  5  inches  wide,  one 
division  of  the  paper  measured  across  its  width  represents  a 
moment  of  10  lbs.,  and,  since  2  tt r  =  36  inches,  one  division 
along  the  length  of  the  paper  =  1°  of  strain. 

In  raising  the  arm  by  the  specimen,  the  moment  of  W  is 
in  equilibrio  with  the  torsional  stress  plus  the  frictional  mo- 
ment of  the  journal  /;  this  last  is  constant  and  is  allowed 
for  in  standardizing  the  machine. 


XV. — M£tALLURGY. 


INTERPRETATION-  OF   THE    RECORD. 

For  torsional  test  this  is  facilitated  by  considerinij  the  spe- 
cimen as  consisting  of  parallel  fibres,  at  first  rectilinear,  and 
elongating  under  stress  in  a  helical  form.  The  general  form 
of  strain  diagrams,  whether  made  by  torsional  or  tensile  test, 
is  so  similar,  that  although  the  following  discussion  partic- 
ularly refers  to  the  results  of  the  torsional  test,  its  application 
may  be  considered  as  general.* 

General  Case. 

The  combined  effect  of  stress  and  strain  is  seen  in  the 
typical  diagrams,  figure  9. 

In  curve  /  the  elastic  limit  is  plainly  shown  at  a.  The 
convexity  of  the  first  portion  is  probably  due  to  the  prelimi- 
nary strain  of  the  exterior  fibres  occurring  in  soft  materials. 

The  line    then   becomes  sensibly  straight,   its   inclination 

determining  the  coefficient  of  elasticity,  -— ,  or  the   rigidity 

of  the  specimen.  Beyond  the  elastic  limit  it  becomes  wavy, 
indicating  deficient  homogeneity  as  to  structure  ;  the  fibres 
are  then  supposed  to  slip.     Having  adjusted  themselves  they 

*  The  following  relation  between  torsional  and  tensile  stress  has  been 
approximately  determined  by  experiment.  Let  T  =  tensile  stress  in 
lbs.  per  square  inch;  Ti  =  torsional  stress  in  lbs. ;  9  =  angle  of  torsion 
in  degrees.     Then,  for  steel  and  probably  for  other  ductile  metals, 

T=  7\  (300 -^\. 
For  cast  iron, 

r=n(soo-^)^|. 

The  extension  of  an  external  fibre  and  the  reduction  in  area  of  cross 
section  corresponding  to  torsional  strain  are  given  in  tables  furnished 
with  the  machine.  For  ultimate  extensions  the  value  of  0  correspond- 
ing to  the  maximum  and  not  to  the  ultimate  ordinate  is  taken. 


10  5tV. — METALLURGY. 


work  together,  as  shown  by  the  subsequent  regularity  of  the 
Hne. 

At  some  point  b  the  stress  is  relaxed,  and  the  pencil  falls  to 
some  point  c  ;  when  the  stress  is  re-applied,  the  pencil  rises  in 
the  line  cb  and  continues  nearly  parallel  to  the  straight  por- 
tion of  the  line  Oa  until  it  reaches  its  former  height  db. 
The  ordinates  then  slowly  increase  until,  by  the  successive 
rupture  of  the  concentric  fibrous  layers,  the  curve  terminates 
at/ 

Note  the  total  work  Oabefg  0\  the  elastic  work  OaL; 
and  the  recoil  dc  and  set  Oc  for  the  stress  db.  The  parallel- 
ism oi  be  to  O'a  shows  the  practical  constancy  of  the  co-- 
efficient  of  elasticity  under  varying  stresses  provided  the  total 
elongation  be  diminished  by  the  set.  By  some,  this  coefficient 
is  considered  the  most  permanent  physical  characteristic  of 
steel,  in  various  forms  of  which  it  has  been  found  to  vary  less 
than  8  per  cent,  in  specimens  whose  elastic  limits  varied  200 
per  cent. 

The  point  ^  is  a  new  elastic  limit,  and  the  entire  line  may 
be  termed  a  locus  of  elastic  limits.  Of  these  the  point  a  is 
called  the  primitive  elastic  limit,  and  the  other  points  various 
special  elastic  limits.  Notice  that  as  these  successively  rise, 
the  potential  work  diminishes.  The  special  elasticity  thus 
produced  by  stress,  as  distinguished  from  the  primitive  elas- 
ticity of  the  specimen,  is  treated  of  in  gun  construction. 

Some  metals  give  a  curve  like  //,  in  which  it  is  difficult  by 
either  of  the  methods  given,  page  3,  to  determine  the  elastic 
limit.  In  such  cases  it  is  generally  taken  as  the  stress  corre- 
sponding to  the  point  of  tangency  of  a  line  inclined  at  45°. 

Graphical  Representation  of  Special  Physical  Properties. 

Considering  the  diagram,  figure  9,  to  represent  that  of  a 
tensile  instead  of  a  torsional 'test,  the  principal  properties  of 
the  specimen  are  graphically  expressed  as  follows: 

The  Tenacity,  or  the  capacity  to  resist  rupture  by  extension, 
is  measured  by  the  maximum  ordinate  at  e.    The  correspond- 


XV. — METALLURGY.  11 

ing  Stress  may  be  greater  than  that  at  which  fracture  finally 
occurs.  In  such  a  case  the  form  of  the  portion  of  the  dia- 
gram, ef,  indicates  probably  the  progressive  rupture  of  the 
final  layers. 

The  Elasticity,  or  the  property  of  resisting  permanent  exten- 
sion or  compression,  as  we  have  seen  may  be  measured  either 
by  an  absolute  quantity,  the  elastic  limit,  or  by  a  rate.  When 
this  rate  is  practically  uniform,  as  in  steel,  page  lo,  the  elas- 
tic limit  alone  may  serve  to  measure  the  elasticity. 

The  Ductility,  or  the  property  of  submitting  to  permanent  ex- 
tension, may  also  be  measured  by  an  absolute  quantity,  O g, 
or  more  exactly.  Oh,  figure  9;  or  by  a  rate.  This  rate- is 
measured  by  the  cotangent  of  the  angle  made  by  the  tangent 
to  the  diagram  at  any  point  beyond  the  elastic  limit  and  the 
axis  of  strains.  This  measure,  although  not  generally 
adopted,  io  important  since  it  illustrates  the  phenomenon 
known  as  the  flow  of  metals  under  stress.  As  seen  in  the 
following  examples,  this  rate  may  vary  not  only  in  degree 
but  also  in  its  sign. 

Ductility,  though  useful  in  such  arts  as  the  drawing  of 
wire  and  of  metallic  cups  like  cartridge  cases,  is  now  regarded 
only  a  secondary  property  of  cannon  metals.  Cannon  are  so 
proportioned  that  the  elastic  limit  is  the  superior  limit  of  the 
applied  forces,  but  the  ductility  of  the  metal  is  thought  to 
give  an  additional  safeguard  against  destructive  explosion. 
But  safety  then  depends  rather  upon  the  potential  work  of  de- 
formation of  which  the  metal  is  capable  than  upon  either  its 
tenacity  or  its  ductility  alone. 

Particular  Cases.     1.  Woods. 

To  illustrate  these  remarks  by  reference  to  materials  the 
physical  properties  of  which  are  more  generally  known  than 
those  of  the  useful  metals,  the  torsional  diagrams  of  the  prin- 
cipal woods  used  in  ordnance  construction  are  represented 
in  figures  10,  11,  12. 

The  woods  are  arranged  from  right  to  left  in  the  order  of 


12  XV.-    METALLURGY. 


their  coefficients  of  elasticity.  This  brings  them  approxi- 
mately in  the  order  of  hardness,  or  stiffness,  black  walnut 
leading. 

These  qualities  fit  this  wood  to  resist  the  abrasion  to  which 
gun-stocks  are  subject,  and  to  give  to  the  easily  bent  gun- 
barrel  its  necessary  support. 

The  elastic  limits  of  cypress  and  black  walnut  are  seen  to 
be  equal,  but  the  cypress  is  much  the  tougher  of  the  two.  It 
appears  to  be  about  equal  to  a  poor  quality  of  oak,  for  which 
wood,  in  the  construction  of  gun-carriages,  it  was  formerly 
used  in  localities  where  oak  could  not  be  procured. 

The  forms  of  the  diagrams  after  passing  the  elastic  limit 
•are  very  characteristic.  In  some  cases,  as  in  ash  and  white 
pine,  the  line  continues  for  some  distance  parallel  to  the  axis 
of  strains.  This  would  indicate  the  use  of  these  woods  for 
pieces  which  being  long  and  slender  are  apt  to  be  bent. 
When  lightness  is  an  object,  as  in  the  former  case  for  wagon 
poles,  sponge  and  rammer  staves,  agricultural-tool  handles, 
and  in  the  latter  case  for  building  purposes,  particularly  of 
railway  carriages,  the  low  density  of  these  woods  makes  them 
highly  esteemed. 

The  sudden  dip  of  dog-wood,  oak,  and  hickory  occurs  in 
most  hard  woods.  It  is  supposed  to  arise  from  the  lateral 
slipping  of  the  fibres,  the  cementing  substance  having  given 
way.  When  this  is  brittle,  as  in  the  resinous  yellow  pine,  a 
very  sharp  depression  is  sometimes  seen. 

In  some  cases,  as  in  dog-wood,  hickory,  and  notably  in 
elm,  the  line  rises  again,  sometimes  exceeding  the  elastic 
limit.  The  rise  is  supposed  to  be  due  to  the  retwisting  of  the 
fibres,  separated  at  the  elastic  limit,  into  a  consistent  whole. 
On  the  other  hand,  the  step-like  decline  of  some  of  the  dia- 
grams indicates  the  brittleness  of  the  corresponding  woods. 

The  surprising  qualities  of  dog-wood  show  that  the  small 
size  of  this  tree  is  the  principal  bar  to  its  utility. 

The  importance  of  testing  machines  is  very  imperfectly  ap- 
preciated among  practical  manufacturers.    This  appears  from 


XV. — METALLURGY.  13 

one  of  the  oak  diagrams  which  was  made  by  a  piece  taken 
from  a  new  gun-carriage  the  stock  of  which  was  broken  in 
two  by  firing. 

2.  Metals. 

The  diagrams  in  figure  13  will  be  referred  to  hereafter  in 
discussing  the  metals  represented  upon  them.  To  avoid 
confusion,  curves  of  similar  metals  are  arranged  in  groups,  a 
new  origin  for  each  group  being  taken  along  the  axis  of 
strains. 


II.  ORDNANCE  METALS. 

The  principal  metals  used  in  Ordnance  manufactures  are. 


Ferreous.  - 


Steel      I  ^'^^' 

'      ( low.  Cupreous  or 

Wrought  Iron,         Kalchoids. 

.  Cast  Iron. 


r  Brasses, 
Bronzes 
and  other  alloys 
of  Cu,  Sn,  Zii. 


Nomenclature. 

For  clearness  of  definition  by  scientific  men,  the  forgeable 
ferreous  metals  are  proposed  to  be  classified  according  to 
their  mode  of  manufacture  and  according  to  their  capacity  to 
harden,  and  are  designated  as  follows: 

1st.  Those  made  from  a  pasty  mass,  by  the  prefix.  Weld. 

2d.   Those  made  by  fusion,  by  the  prefix,  Ingot. 

3d.  Those  which  will  harden  and  temper  by  the  usual 
treatment  of  steel,  by  the  suffix,  Steel. 

4th.  Those  which  will  not  sensibly  harden,  by  the  suffix, 
Iron. 

5th.  The  only  unforgeable  ferreous  cannon  metal  is  cast 
iron,  known  in  the  crude  state  as  pig-iron  and  after  remelt- 
ing,  as  castings. 

This  classification  affords  the  following  scheme; 


14 


XV.— METALLURGY. 


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XV. — METALLURGY.  15 


Relative  Importance. 

Owing  to  their  peculiar  adaptability  to  the  demands  of 
construction,  the  ferreous  ingot  metals  are  gradually  super- 
seding all  others,  and  the  time  when  they  will  be  altogether 
employed  except  for  subordinate  purposes  is  delayed  only  by 
our  imperfect  knowledge  of  their  properties.  These  metals, 
under  the  common  name  of  steel,  already  cover  in  their 
application  the  wide  range  between  castings  for  the  frames  of 
iron-clads,  weighing  many  tons,  figure  14,  and  horseshoe 
nails,  the  successful  making  of  which  was  formerly  considered 
the  most  severe  test  of  the  quality  of  wrought  iron.  The 
ages  of  stone,  bronze,  cast  and  wrought  iron  have  been  suc- 
ceeded by  the  age  of  steel. 

On  this  account  the  following  discussion  will  relate  princi- 
pally to  steel.  As  a  cannon  metal  it  has  only  recently  come 
into  favor,  having  been  considered  brittle  and  untrustworthy. 
It  is  largely  due  to  the  patient  genius  of  Krupp  and  Whit- 
worth  that  this  prejudice  has  been  overcome. 

As  an  example  of  the  quality  of  modern  gun  steel  may  be 
mentioned  the  fact  that  it  was  found  impossible  to  break  a 
gun  hoop  under  a  drop  giving  a  blow  of  nearly  100  ft.-tons, 
the  arrangement  being  represented  in  figure  15.  Sixty  or 
seventy  blows  shortened  the  vertical  diameter  only  half  an 
inch. 


III.  PROPERTIES. 

The  useful  properties  of  metals  have  regard  to  their 

1,  Homogeneity, 


I.  Constitution. 
{Jo  be.) 


I.   Chemical  as  to  i  o'  n 

(2,  Composition. 

( 1,  Homogeneity, 

II.   Physical  as  to   -J  2,  Structure, 

(  3,  Strain. 


16  XV. — METALLURGY. 


II.  Capacity  for 
resisting. 
{To  do.) 


I.   Tensile  j  1,  Tenacity, 

Stress,  or    ( 2,  Ductility. 

II.  Compressive  j  1,  Incompressibility, 

Stress,         I  2,  Hardness. 

III.  Either  j  1,  Elasticity, 

Stress,  or    (  2,  Homogeneity. 


III.   Facility  for  being 
worked. 
{To  suffer.) 


C 1,  Fusibility, 

Hot,  or  \  2,  Weldability. 

(  3,  Malleability  (also  cold). 

Cold,  or     1,  Annealability. 


/.  CONSTITUTION  OF  STEEL. 
Metals  should  be  homogeneous  as  to  composition  and  struc- 
ture so  as  to  be  homogeneous  as  to  strain.     Those  which 
have  been  fused  are  the  most  homogeneous ;  but  even  they 
may  be  imperfect,  both  chemically  and  physically,  as  follows : 

I.    CHEMICAL  CONSTITUTION. 

1.  Homogeneity. 

Pure  iron  can  rarely  be  produced  except  by  the  methods 
of  the  laboratory,  and  therefore  in  exceedingly  small  quanti- 
ties. In  practice  it  is  combined  with  the  most  useful  elements 
by  heat,  the  fusibility  of  the  alloy  usually  increasing  with  the 
number  of  elements  contained.  Fused  metals  in  general  are 
imperfect  alloys,  the  constituents  of  which  tend  to  arrange 
themselves  according  to  their  specific  gravities.  Due  to  the 
property  of  liquation,  certain  of  the  most  fusible  alloys  of 
steel  are  found  near  the  core  of  the  ingot  in  greater  propor- 
tion than  elsewhere.  Thus,  in  a  steel  ingot  the  parts  first 
solidified  represent  most  nearly  its  average  composition,  the 
centre  of  the  bottom  being  the  softest  and  that  near  the  top 
the  hardest,  since  the  fusibility  and  the  hardness  of  the  alloy 
increase  with  the  percentage  of  C* 

*  Order  of  Oxidation. 

Reactions  during  fusion  depend  so  much  upon  the  order  of  oxidation 
of  the  constituents  of  pig-iron  that  the  following  approximate  relation 
should  be  learned: 


XV. — METALLURGY.  17 


The  segregation  of  the  Kalchoids  is  very  objectionable. 

2.  Composition. 

The  following  elements  occur  in  iron  alloys : 
1.  Carbon  and  iron  as  the  principal  constituents  make  the 
steel  best  suited  for  general  purposes.  It  has  often  been  tried 
to  replace  or  supplement  the  action  of  carbon  by  other  ele- 
ments such  as  silicon,  tungsten,  chromium,  nickel,  etc.,  but 
for  general  purposes  carbon  steel  is  far  the  most  important. 

As  a  rule,  the  greater  percentage  of  carbon  up  to  about 
1.5  (and  even  2  5  per  cent.),  or  the  higher  the  grade, 

The  more —  The  less — 

1.  hard  and  elastic  ;  1.  dense; 

2.  tenacious ;  2.  ductile  ; 

3.  brittle ;  3.  weldable  ; 

4.  fusible;  4.  forgeable,  does  steel  be- 

5.  expansible  by  heat,  does  come. 

steel  become. 

The  terms  high  and  lotv  referring  to  the  grade  of  steel,  or 
per  cent,  of  C  contained,  are  loosely  applied,  but  the  tendency 
is  to  draw  the  line  at  0.35  per  cent.,  where  hardening  by  heat- 
ing followed  by  rapid  cooling  becomes  perceptible.  The 
following  table  exhibits  the  classification  according  to  use. 
So  much  depends  upon  the  percentage  of  hardening  constitu- 
ents other  than  C,  and  upon  the  treatment  of  the  steel  in 
manufacture,  that  the  relation  expressed  is  only  approximate. 


1.  Silicon.  5.  Iron. 

2.  Manganese.  6.  Phosphorus,  in  presence  of  an  acid 

3.  Phosphorus,  in  presence  of  slag;    i.  ^.,  one  containing  an 

an  oxidizing  basic  slag.  excess  of  S  i  O^. 

4.  Carbon. 

These  and  other  following  relations  depend  so  much  upon  existing  tem- 
peratures and  conditions  that  they  are  expressed  in  the  most  general  terms. 


18 


XV. — METALLURGY. 


Grade. 


TABLE  IL        GRADES  OF  STEEL. 

Per  Cent,  of  Carbon.  Application. 


Low. 


High. 


Mild, 

Hard, 

Extra  hard, 
Tool, 

Extra  Tool, 
Die, 


Extra  mild,    0.05 — 0.20    Boiler  plates  to  be  flanged, 

bridge  material. 
0.20 — 0.35    Railroad  axles,  gun  bar- 
rels, etc. 

0.35 — 0.50    Rails,  cannon,  etc. 
0.50 — 0.65    Springs,  saws,  etc. 
0.75 — 1.00    Chisels,  cutters,  etc. 
1.00 — 1.20    Files  and  very  hard  tools. 
2.50    Wire    drawing,  to   resist 
abrasion. 

Carbon  is  generally  supposed  to  exist  in  steel  in  two  princi- 
pal forms:  1.  Cement  carbon^  characteristic  of  annealed  or 
softened  steel,  and  2.  Hardening  carbo?i,  characteristic  of 
hardened  steel.  The  former  is  insoluble  and  the  latter  is 
soluble  in  dilute  H^  SO^.     See  page  48. 

The  following  elements  are  admitted,  either  of  necessity  or 
as  Si  physic ;  i.  e.,  replacing  something  more  harmful  or  pro- 
ducing a  beneficial  effect. 

2.  Silicon  tends  to  displace  C  from  combination,  and  to 
confer  its  properties,  although  in  a  less  degree. 

It  restores  ''burned"  or  "rotten"  steel  by  forming  with 
the  particles  of  iron  oxide,  to  the  dissemination  of  which 
this  condition  is  often  due,  a  fusible  slag : 

{Fe^  O^  +  Siz=zFe  Si  O^  +  Fe), 

As  Si  increases  the  solvent  power  of  steel  for  gases,  and, 
by  reducing  the  iron  oxide  present  in  the  hquid  steel,  prevents 
the  formation  of  CO  it  also  prevents  the  honeycombing  or 
vesiculation  of  the  metal  from  the  ebullition  of  the  gases 
while  the  metal  is  becoming  soUd. 

If  uncombined,  Si  O^  may  remain  as  grit,  which  is  injuri- 
ous to  the  strength  of  the  metal  and  destructive  to  cutting 
tools. 


XV. — MEtALLtJRGY.  19 


When  in  excess,  Si  makes  steel  brittle.  This  is  generally- 
true  of  the  non-ferreous  ingredients  of  the  alloy. 

3.  Manganese,  unlike  Si,  tends  to  make  C  combine  with 
iron ;  like  Si,  it  tends  to  replace  C  functionally,  but  much  less 
energetically. 

Afn  resembles  Si  as  a  reducing  agent,  and  forms  with  it  and 
iron  oxide  a  very  fluid,  cleansing,  slag. 

The  physical  properties  it  confers  vary  with  the  proportion 
present.  With  from  3  to  6  per  cent,,  the  steel  becomes  very- 
hard  and  brittle ;  but  with  from  7  to  20  per  cent,  the  steel 
becomes  very  tough  and  strong. 

Some  Mn  is  necessary  to  prevent  hoi-shortness,  or  the  tend- 
ency to  disintegrate  when  forged,  even  when  no  6*  is  present. 
It  also  acts  as  an  antidote  to  S,  by  forming  Mn  S,  which  is 
insoluble  in  melted  steel. 

4.  Phosphorus  make  steel  cold  short,  or  brittle  at  ordinary 
temperatures.  It  can  be  removed  only  by  some  basic  process, 
as  follows :  Since  the  ordinary  silicious,  or  acid,  lining  would 
prevent  the  oxidation  of  P,  and,  by  wasting  the  iron,  would 
increase  the  proportion  in  which  P  remained ;  in  the  basic 
process  the  furnace  is  lined  with  dolomite  brick.  Iron  ore 
and  (for  economy)  limestone  are  added  to  the  charge,  so  that 
the  phosphoric  slag  that  is  formed  may  continue  basic. 

The  presence  of  Mn  and  Si  in  the  pig  iron  from  which 
washed  pig  is  thus  formed,  protects  from  oxidation  the  C  that 
it  contains,  and  therefore  maintains  the  fluidity  of  the  charge, 
until  the  Mn  and  Si  are  consumed.  When  this  happens  and 
the  bath  boils  with  CO,  the  washed  metal  is  cast  into  pigs 
containing  only  about  0.1  of  the  original  P. 

So  much  C  is  retained  that  (after  grading  it  by  analysis) 
the  washed  pig  is  easily  remelted  in  further  processes  relating 
to  the  manufacture  of  steel. 

These  processes  permit  the  use  of  pig  iron,  which  was 
formerly  too  high  in  P. 


20  XV. METALLtfRGV. 


When  added  to  the  Kalchoids,  P  removes  their  greatest 
enemy,  oxygen. 

5.  Sulphur  also  is  very  difficult  to  remove,  although  the 
hot-shortness  that  it  produces  may  be  corrected  with  Mn  or 
eliminated  by  Ca  F^. 

6.  Chromium  increases  the  hardness  of  steel  without  im- 
pairing those  qualities,  such  as  ductility  and  malleability, 
which  are  incompatible  with  the  hardness  resulting  from  high 
carbon. 

7.  Aluminium  is  said  to  increase  the  fluidity  of  low  steel, 
and  even  of  weld  iron,  in  a  remarkable  degree,  thus  permit- 
ting the  metal  to  be  cast  without  danger  from  vesiculation. 
The  fluidity  of  the  metal  in  the  mold  permits  the  escape  of 
the  occluded  gases.  Its  action  on  iron  oxide  resembles  that 
of  Si. 

A  new  alloy  known  as  Mitis  metal,  which  is  thus  formed, 
may  be  cast  into  the  most  complex  forms. 

8.  Nickel  remarkably  increases  the  useful  properties  of 
steel ;  the  result  varying  with  the  percentage  as  in  Mn.  The 
armor  plates  now  (1891)  preferred  are  made  of  nickel  steel. 

9.  Copper.  When  thoroughly  deoxidized,  steel  may  be 
improved  by  the  addition  of  Cu,  although  it  is  thought  by 
some  that  it  makes  steel  hot-short, 

II.    PHYSICAL    CONSTITUTION. 

1.  Homogeneity. 

As  in  chemical  composition,  no  fused  metal  is  naturally 
physically  homogeneous,  either  in  structure  or  in  strain. 
These  properties  may  be  so  modified  by  after-treatment  that 
the  following  comparisons  apply  to  non-forgeable  metals  as 
ordinarily  cooled  after  fusion ;  and  to  forgeable  metals  when 
annealed.    This  is  the  standard  condition  for  their  comparison* 

2.  Structure. 

The  structure  is  juaged  of  by  the  appearance  of  the  frac- 
tures; for  exact  comparison  these  should  be  similarly  pro- 


XV. — METALLURGY.  21 


duced.  By  varying  the  method  of  breaking  it,  the  fracture 
of  a  bar  of  wrought  iron  may  be  made  either  crystalline  or 
fibrous  within  a  few  inches  of  its  length. 

Crystallization.  It  is  assumed  that  ingot  metals  are  crystal- 
line, and  weld  metals  fibrous,  although  the  ultimate  crystal- 
line forms  are  doubtful.*  Thus,  the  former  may  be  supposed 
to  consist  of  normal  crystals,  and  the  latter  of  distorted  crys- 
tals cemented  by  a  film  of  slag. 

Normal  crystals  are  supposed  to  be  formed  like  those  of 
soluble  salts ;  the  more  slowly  and  quietly  they  are  cooled 
from  fusion,  the  larger  and  weaker  they  are,  and  conversely. 
(Bioxam,  Art.  38.) 

The  crystalline  axes  are  found  perpendicular  to  the  cooling 
surfaces,  so  that  surfaces  of  weakness  are  formed  at  the  junc- 
tion of  inclined  systems.  See  figures  16,  17.  For  this  reason 
the  corresponding  surfaces  should  be  united  by  gradual  curves 
so  as  to  distribute  strains  which  would  otherwise  be  localized. 
Sharp  re-entrant  angles  should  be  avoided  in  all  structural 
masses,  even  the  non-crystalline. 

Vesiculation.  Another  structural  form  arises  from  the  oc- 
clusion of  air  and  other  gases  during  the  casting.  This  causes 
^'' blow -holes,''  which  increase  with  the  viscidity  of  the  fluid 
mass.  On  the  other  hand,  when  the  metal  is  free  from  blow- 
holes, an  axial  cavity  is  formed,  due  to  internal  strain.  This 
is  known  as  3.  pipe.     Figure  18. 

3.  Strain. 

Differences  in  the  rate  of  cooling  throughout  a  fluid  mass 
produce  internal  strain,  the  parts  first  solidifying  being  com- 
pressed by  their  adhesion  to  the  layers  cooling  subsequently, 
which  last  are  reciprocally  extended.     Similar  effects  follow 


*  By  some  the  primitive  structure  of  ingot  steel  is  supposed  to  be  that 
of  globules  of  the  alloy  imbedded  in  a  mo  e  highly  carbonized  cement. 
This  is  called  the  Cellular  Theory. 


22  XV. — METALLURGY. 

unequal   heating.     The  importance  of  this   principle  is  fre- 
quently apparent,  particularly  in  dealing  with  iron  castings. 

//.  CAPACITY  FOR  RESISTING  STRESS, 

Properties. 

Owing  to  the  facility  of  referring  other  stresses  to  a  tensile 
stress,  this  alone  is  generally  considered,  the  incompressibiuty 
of  cannon  metals  being  sufficiently  guaranteed  by  their  com- 
bined hardness  and  tenacity. 

The  principal  properties  of  1.  tenacity,  2.  elasticity,  3. 
ductility,  and  4.  toughness,  have  already  been  discussed. 

5.  Hardness  is  properly  the  property  of  resisting  penetra- 
tion ;  combined  with  tenacity,  with  which  it  is  almost  invari- 
ably associated,  it  renders  cannon  metal  incompressible  by 
powder  pressure,  and  in  itself  resists  abrasion,  erosion  and 
impact  from  hostile  shot. 

Steel  may  be  artificially  hardened  by  heating  it,  followed 
by  its  rapid  cooling.  Steel  and  bronze  may  also  be  hardened 
by  their  compression  in  a  cold  state ;  externally  by  rolling 
and  internally  by  mandreling,  which  consists  in  forcing 
through  a  hole  conical  plugs  of  slowly  increasing  diameter. 

It  is  noteworthy  that  by  heating  and  rapid  cooling,  brass, 
bronze  and  the  high  Mn  steel,  p.  19,  are  softened, 

III,  FACILITY  FOR  BEING  WORKED, 

1.  Fusibility. 

This  diminishes  the  number  of  joints  in  a  given  structure, 
and,  other  things  being  equal,  increases  its  cheapness,  homo- 
geneity and  strength.  Recent  advances  in  mechanical  en- 
gineering have  been  principally  due  to  the  large  units  of  con- 
struction afforded  by  the  capacity  and  power  of  modern 
furnaces.  Thus  steel  is  replacing  wrought  iron,  which  is 
formed  by  agglutination. 


XV. — METALLURGY.  23 


2.  Malleability, 

or  to  the  power  to  endure  hammering  or  roUing,  particularly 
at  high  temperatures,  enables  metals  to  be  forged  into  special 
shapes,  thereby  improving  the  quality  of  the  metal  and  reduc- 
ing the  labor  of  finishing.  When  combined  with  fusibility, 
it  gives  advantages  peculiar  to  steel. 

3.  Weldability, 

or  the  power  of  adhesion  at  high  temperatures  between 
masses  is  characteristic  of  wrought  iron  and  low  steel.  It  is 
upon  this  property  that  the  manufacture  of  wrought  iron 
depends.  This  property  in  construction  is  inferior  to  fusi- 
bility and  hence  is  not  utilized  for  steel  except  in  small  masses. 

The  process  of  electric  welding  is  now  (1891)  successfully 
employed.  It  consists  in  sending  a  powerful  low-pressure 
current  through  the  abutting  surfaces  of  the  pieces  to  be 
united.  The  resistance  at  the  points  of  contact  raises  the 
neighboring  metal  to  the  temperature  of  incipient  fusion; 
pressure  being  then  applied,  fresh  surfaces  are  successively 
brought  into  contact.  Owing  to  the  high  temperature  of  the 
first  contacts,  the  current  is  mainly  conveyed  through  the  new 
ones  and  so  on  until  a  homogeneous  joint  is  formed. 

Hollow  projectiles  are  thus  made  from  steel  tubing  welded 
to  a  point  and  a  base.  It  is  even  proposed  to  heat  finished 
pieces  locally,  so  as  to  permit  them  to  be  bent  or  tempered 
without  injury  from  the  hammer  or  the  fire. 

4.  Annealability, 

or  the  power  to  become  soft,  facilitates  reduction  to  size  by 
cutting  tools.  All  the  cannon  metals  can  be  softened  by 
annealing,  but  to  steel  only  can  the  necessary  hardness  be 
restored,  except  mechanically. 

Grindi?ig.  It  fortunately  happens  that  hardened  steel, 
which  can  cut  all  the  other  useful  metals,  can  itself  be  abraded 
by  grinding  almost  as  easily  as  when  soft. 


24  XV. — METALLURGY. 


This  permits  the  change  of  form  which  often  follows  hard- 
ening to  be  corrected  by  the  use  of  either  natural  or  artificial 
grindstones.     See  Chapter  XVII,  page  14 
CONCLUSION. 

The  relative  standing  of  the  five  cannon  metals   may  be 
roughly  indicated  as  follows  : 

^STEEL->         , IRON > 

High,     Low.         Wrought,  Cast.        Bronze. 

1.1  f?l^„aS'/1  ^  ^  3  4  5. 

t!  5  -(  Homogeneity,  I  1  o  A.  ^  f? 

2  %  I  Hardness,  normal,  f  ^  ^  ^  d  o. 

tn  ^  1^  Ductility,  4  3  15  2. 


f  Fusibility,  3        4  —  3 

Malleability,  3        2  1  — 


O   cJ 
cr 


C    (U 

•^  §  s(  Weldability,  —       2  1 


Annealability  or      ^  ^         o  q 

variable  hardness,  f 

This  indicates  why  bronze  and  the  irons,  which,  owing  to 
their  workability,  were  until  recently  the  only  cannon  metals, 
are  now  obsolete. 

IV.  MANUFACTURE  of  the  FERREOUS  METALS. 

/.  CAST  IRON, 

Varieties. 

The  gray  pig  is  known  diS  foundry  or  77ielting  irow,  the  white 
pig  as  forge  iron ;  the  latter  is  useful  only  for  conversion 
into  wrought  iron.     Mottled  pig  is  an  intermediate  variety. 

Remelting. 

To  obtain  strong  castings,  the  foundry  pig  is  ordinarily 
remelted  and  run  into  molds  of  the  required  shape. 

The  specific  gravity  of  pig-iron  is  about  7.00,  and  its 
tenacity  about  16,000  pounds  to  the  square  inch,  but,  when 
remelted,  the  specific  gravity  is  increased  to  about  7.25,  and 
the  tenacity  about  doubled. 

The  remelting  is  effected  in  cupola  or  reverberatory  fur- 
naces, according  to  the  kind  of  fuel  available  and  the  size 
and  quality  of  the  casting  required.     It  is  always  necessary 


XV. — METALLURGY.  25 


to  melt  as  quickly  as  possible,  and  with  the  least  consump- 
tion of  fuel.     This  usually  requires  artificial  blast. 

In  Cupolas.  The  cupola  furnace  is  generally  employed  ; 
its  size  depends  upon  the  amount  of  metal  to  be  melted  at  a 
time,  and  upon  the  kind  of  fuel. 

A  cupola  extensively  used  is  of  the  Mackenzie  pattern,  fig- 
ure 19.  It  consists  of  the  iody  B,  of  elliptical  cross  section, 
made  of  thick  sheet-iron  lined  with  fire-brick ;  this  is  sur- 
mounted by  a  conical  hood  H,  terminating  in  the  chimney  C. 
The  blast  is  admitted  through  an  annular  tuyere  extending 
around  the  bottom  part  of  the  furnace.  The  charge  is  intro- 
duced at  the  door  D,  and  the  molten  metal,  accumulated  in 
the  hearth  H,  is  drawn  off  at  the  spout  S,  and  carried  to  the 
mold  through  a  channel  or  by  means  of  ladles. 

The  elliptical  section  of  the  body  in  combination  with  the 
annular  tuyere  increases  the  capacity  of  the  furnace  for  a 
given  intensity  of  blast ;  the  object  being  to  maintain  a  high 
temperature  in  the  vertical  plane  containing  the  transverse 
axis  of  the  ellipse,  along  which,  for  regularity  of  feeding,  it 
is  desirable  to  cause  the  contents  of  the  furnace  to  descend.     I 

The  cupola  furnace  saves  fuel,  labor  and  time,  and  fur- 
nishes a  continuous  supply  of  iron,  which,  since  the  carbon 
in  the  pig-iron  is  not  diminished  by  melting,  is  liquid  and 
therefore  of  the  quality  suited  to  foundry  purposes. 

The  charge  consists  of  pig-iron  and  generally  scraps  of 
cast  iron,  a  flux,  and  the  fuel ;  for  the  latter,  coke  and  char- 
coal are  best,  though  anthracite  is  generally  employed. 

In  Reverberatory  Furnaces.  Reverberatory  furnaces  are 
principally  used  for  the  production  of  large  castings,  and  are 
specially  adapted  to  all  such  as  require  great  strength.  Their 
use  is  sometimes  necessitated  if  the  fuel  at  disposal  contains 
sulphur. 

The  name  is  derived  from  the  arch  which  beats  back  the 
flame  on  the  metal  to  be  heated. 

The  furnace,  figure  20,  is  built  of  fire-brick  bound  strongly 
together  by  iron  bars  or  plates ;  the  hearih  H  is  of  refractory 


S6  XV. — METALLURGY. 


brick  covered  with  a  thick  layer  of  Bre-sand  ;  the  grate  G  is 
large,  that  a  great  volume  of  flame  from  the  fuel  may  be 
drawn  over  the  bridge  -5  and  through  the  furnace ;  for  this 
purpose  the  chimney  C  is  made  very  tall  when  no  artificial 
blast  is  used.  The  metal  is  introduced  at  the  charging  doors 
D,  D\  and,  when  melted,  is  drawn  off"  at  the  tap-hole  (h). 

The  dimensions  of  the  furnace  depend  chiefly  on  the  charge 
of  iron  and  quality  of  the  fuel.  They  are  of  correct  propor- 
tions if  a  nearly  uniform  temperature  be  produced  in  all  parts 
of  the  furnace. 

Unlike  the  cupola,  this  furnace  allows  the  iron  to  be  kept 
liquid  for  any  length  of  time ;  and,  as  the  fuel  is  not  in  con- 
tact with  the  metal,  and  carbon  and  silicon  are  removed  by  the 
air,  a  stronger  iron  results.  On  the  other  hand,  it  does  not 
admit  of  constant  casting,  and  involves  a  great  loss  of  iron 
by  oxidation  ;  owing  to  these  circumstances  and  to  the  greater 
consumption  of  fuel,  such  furnaces  are  used  only  in  large 
foundries,  and,  whenever  practicable,  are  replaced  by  cupolas 
of  large  size. 

Properties  of  Iron  for  Castings. 

The  color  and  texture  of  a  casting  depend  greatly  on  its 
size,  and  on  the  rapidity  with  which  it  has  been  cooled,  and 
upon  its  composition.  As  small  castings  cool  quickly  they 
are  almost  always  white,  and  the  surface  of  large  castings 
partakes  more  of  the  quality  of  white  iron  than  does  the 
interior. 

When  gray  iron  is  melted,  the  particles  of  graphite  to 
which  its  color  is  due  are  dissolved  by  the  liquid  iron,  and  if 
it  be  poured  into  a  cold  iron  mold  so  as  to  solidify  quickly, 
the  exterior  of  the  casting  will  present  much  of  the  hardness 
and  appearance  of  white  iron,  the  sudden  cooling  having  pre- 
vented the  separation  of  the  graphite.  This  is  particularly 
apt  to  follow  the  presence  of  manganese  in  the  iron. 

At  the  instant  of  solidification  gray  iron  expands  more 
than  white,  giving  a  casting  with  sharp  edges  and  a  convex 


XV. — METALLURGY.  ^? 


surface;  and,   as  it   subsequently  contracts   less,   the   initial 
strains  due  to  cooling  are  less. 

White  iron  gives  a  casting  with  a  concave  surface,  and 
mottled  iron  one  with  a  plane  surface,  the  edges  slightly 
rounded. 

SPECIAL    CAST    IRONS. 

Malleable  Cast  Iron. 

By  extracting  a  portion  of  the  carbon  from  cast-iron  its 
composition  is  assimilated  to  that  of  wrought  iron  and  its 
toughness  increased  ;  the  result  is  known  as  malleable  cast 
iron. 

The  castings  to  be  softened  are  packed  with  powdered 
haematite  ore,  or  scales  of  oxide  of  iron,  and  the  temperature 
raised  gradually  to  a  red  heat ;  this  is  continued  from  three  to 
five  days  according  to  the  thickness  of  the  layer  of  malleable 
metal  required. 

When  withdrawn  from  the  furnace,  articles  so  heated  have 
the  appearance  of  ordinary  malleable  iron,  but  are  lighter 
in  color ;  their  fractured  surfaces  are  white  and  finely  granular, 
occasionally  having  a  silky  appearance  like  that  exhibited  by 
soft  steel. 

The  principal  application  of  this  process  is  to  such  articles 
as  buckles,  bits,  stirrups,  keys,  etc. 

Case-hardening.  The  stratum  of  malleable  metal  on  the  sur- 
face may  be  converted  into  steel  by  the  process  of  case-hard- 
ening, which  consists  in  a  similar  heating  in  contact  with  ani- 
mal charcoal,  after  which,  while  still  hot,  the  casting  is  plunged 
into  water  or  oil.  This  process  is  applied  also  to  articles  of 
wrought  iron,  such  as  the  parts  of  small-arms  in  which  it  is 
desired  to  have  a  tough,  somewhat  soft  interior  protected 
from  friction  or  blows  by  a  hard  surface.  The  hammer  and 
breech-block  of  the  Springfield  rifle  are  so  treated. 


28  XV.— METALLURGY. 


SPECIAL    ALLOYS. 

Varieties. 

Spiegeleisen  or  Spiegel  {Sp)  and  Ferro- Manganese  (FM) 
may  be  regarded  as  varieties  of  white  cast  iron  alloyed  with 
a  varying  proportion  of  Mn,  That  which  contains  over  20 
per  cent,  of  Mn  is  known  as  FM.  When  Mn  amounts  to 
80  or  90  per  cent.,  it  may  consume  by  spontaneous  oxidation. 

The  price  of  FM  increases  with  its  richness  in  Mn,  for  this 
limits  the  choice  of  ores  and  increases  the  temperature  of 
reduction  and  fusion,  and  the  loss  by  volatilization  and  oxi- 
dation. 

Silicon- Spiegel  and  Ferro-Silican  are  similar  alloys,  but  con- 
tain much  more  Silicon. 

The  following  table  exhibits  roughly  the  ingredients  of 
some  of  the  principal  special  alloys,  and  illustrates  the  state- 
ments previously  made  as  to  the  effects  of  Mn  and  Si  upon 
the  proportion  of  iron  in  combination. 

Note  the  gain  in  C  as  Mn  increases,  and  its  loss  as  Si 
increases. 

TABLE. 

Name.  8%  Mn  C  Fe^ 

(combined.)      etc. 

1.  Ferro-Manganese,  80  7  13 

2.  "             '*  60  6  34 

3.  Spiegel-Eisen,  1  10  5  84 

4.  Silico-Spiegel,  10  20  2  68 

5.  Ferro-Sihcon,  10  2  88 

Use.        / 

These  alloys  are  manufactured  principally  for  the  steel 
makers,  being  used  by  them  to  improve  the  quality  of  steel 
while  in  a  state  of  fusion. 

Generally  speaking,  Ferro-Manganese  is  used  when  the 
quantity  of  C  necessary  is  small  as  compared  with  the  Mn 
required ;  and  conversely  with  Spiegel-Eisen,  although  in  the 


XV. METALLURGY.  29 


latter  case  C  may  be  added  directly  in  a  pulverulent  form,  or 
in  a  pure  pig  iron. 

The  Silicon  irons  are  principally  used  to  prevent  vesicula- 
tion;  No.  4  is  preferred  to  No.  5,  as  the  increase  in  Mn 
causes  the  Si  to  more  thoroughly  combine  with  the  steel  and 
improves  its  structure. 

//.  MODERN  MANUFACTURE  OF  WROUGHT  IRON. 

Principles. 

The  great  cost  of  the  hand  labor  engaged  in  the  ordinary 
process  of  puddling  has  led  to  the  use  of  mechanical  means 
for  accomplishing  this  result.  The  two  principal  processes 
are  those  of  Danks  and  Perfiot.  Their  common  feature  is 
the  continuous  rotation,  by  mechanical  means,  of  the  vessel 
containing  the  charge,  thus  avoiding  the  loss  in  time  and 
power  due  to  the  reciprocating  action  of  the  puddler's  rabble  ; 
and  diminishing  the  number  of  skilled  workmen  required. 

The  principle  involved  in  these  processes  is  that  given  in 
Bloxam,  Art.  219,  viz.:  That  when  cast  iron  is  heated  in  con- 
tact with  iron  oxide,  the  C  and  Si  in  the  iron  take  O  mainly 
from  the  iron  oxide  in  the  fettling  of  the  furnace.  The  C 
passes  off  as  CO  and  CO^,  and  the  Si  as  an  iron  silicate  or  slag. 
Danks  Process. 

The  furnace,  Figure  22,  consists  of  a  horizontal  drum,  revolv- 
ing on  rollers  and  lined  with  2.  fettling  of  lumps  of  haematite 
ore  set  in  a  fused  paste  of  the  same  ore.  The  flame  from  a  sta- 
tionary fireplace  plays  through  one  end  of  the  drum  and  passes 
off  through  a  movable  flue  at  the  other  end.  The  removal  of 
the  flue  permits  the  drum  to  be  charged  and  emptied. 

For  economy. the  furnace  maybe  charged  with  melted  iron, 
either  directly  from  a  blast  furnace  or  from  a  cupola.  If 
charged  cold  the  rate  of  revolution  is  slow  while  melting;  it 
is  increased  while  boiling,  during  which  the  fettling  and  the 
flame  rapidly  oxidize  the  C  and  Si  exposed  by  the  rolling  of 
the  pasty  mass  and  the  adherent  film  and  drip  from  that 


30  XV, — METALLURGY. 


which  is  melted.  The  drum  is  stopped  to  tap  the  cinder.  It 
is  then  revolved  more  rapidly  than  before,  draining  the  pasty- 
mass  until  it  begins  to  ball.  The  large  lumps,  carried  around 
by  adhesion,  fall  on  those  at  the  bottom  and  help  to  work  out 
the  cinder.  This  is  more  thoroughly  done  afterward  by  the 
usual  methods. 

Pernot  Process. 

The  pan  revolves  under  a  stationary  cover,  on  an  axis  in- 
clined about  5°  or  6°  to  the  vertical,  see  figure  85.  The  fet- 
tling is  thus  exposed  alternately  to  the  flame  and  to  the  metal, 
the  film  of  oxidized  iron  thus  formed  passing  under  the  fluid 
mass  and  assisting  the  reduction.  Balling  still  has  to  be  done 
by  hand ;  but  the  process  uses  less  coal  than  the  ordinary 
one,  and  the  furnace  can  be  more  easily  repaired. 

These  processes  are  losing  their  importance  in  consequence 
of  the  rapidity  with  which  steel  of  various  grades  is  supplant- 
ing wrought  iron. 

///.    MANUFACTURE  OF  STEEL. 
I.    IN    SMALL   MASSES. 

1.  Weld  Steels. 

Puddled  Steel.  Puddled  steel  is  made  by  stopping  the  pro- 
cess of  puddling  when  the  de-carbonization  of  the  cast  iron 
has  sufficiently  advanced.  It  is  principally  used  for  conver- 
sion into  other  kinds  of  steel. 

Blister  Steel,  which  is  made  by  cementation,  being  full  of 
fissures  and  cavities,  is  fit  only  for  a  few  rough  purposes,  as 
for  facing  hammers ;  most  of  that  made  is  used  for  conversion 
into  other  kinds  of  steel. 

Tilted  Steel,  When  bars  of  blister  steel  are  heated  or 
hammered  into  bars  under  a  tilt  hammer^  Figure  40,  the  pro- 
duct is  termed  tilted  steel ;  spring  steel  is  thus  prepared. 

Shear  Steel.  Shear  steel  is  produced  by  cutting  bars  of 
blister  steel  into  convenient  lengths,  and  piling,  heating,  and 
welding  them  under  a  hammer,  whereby  is  obtained  a  bar  of 


XV. METALLURGY.  31 

uniform  quality  known  as  single  shear  steel ;  the  quality  of 
the  metal  is  still  further  improved  by  a  repetition  of  the  pro- 
cess, forming  a  bar  of  double  shear  steel.  The  oftener  the 
process  is  repeated,  the  more  uniform  is  the  resulting  steel. 

Shear  steel  is  capable  of  receiving  a  better  edge  and  a 
higher  polish  than  blister  or  spring  steel;  when  well  prepared, 
it  is  not  much  inferior  to  crucible  steel.  It  is  very  exten- 
sively used  in  work  where  steel  and  iron  have  to  be  united  by 
welding,  as  in  axe-bits  and  scissors. 

2.  Crucible  Steel. 

Although  blister  steel  by  repeated  working  under  the  ham- 
mer acquires  a  tolerably  homogeneous  structure,  it  is  still 
further  improved  by  fusion.  The  process,  invented  a  century 
ago,  still  remains  in  principle  unaltered.  Fragments  of  blis- 
ter steel  are  melted  in  crucibles,  figure  23,  covered  to  exclude 
the  air,  and  the  liquid  poured  into  cast-iron  ingot  molds  of 
the  shape  and  size  required.  These  ingots  usually  contain 
cavities;  they  are  gotten  rid  of  by  heating  the  mass  and  ham- 
mering it  into  coijipact  and  homogeneous  bars. 

Most  crucible  steel  is  now  made  direct  from  bars  of  the 
best  wrought  iron  ;  they  are  broken  and  placed  in  the  cruci- 
ble with  a  small  quantity  of  charcoal  or  pig  iron,  the  amount 
varying  according  to  the  grade  of  steel  required ;  some  alloy 
of  manganese  is  subsequently  added.  The  preliminary  frac- 
ture of  the  material  charged  facilitates  its  classification  and 
increases  the  uniformity  of  the  product. 

Properties. 

In  forging,  crucible  steel  should  never  be  raised  beyond 
a  certain  temperature,  varying  inversely  with  the  grade, 
or  it  will  become  brittle.  It  is  difi&cult  to  weld,  as  it  is  usu- 
ally high  in  carbon. 

If  a  small  quantity  of  manganese  be  added  to  the  molten 
metal,  the  steel  will  be  more  forgeable  and  may  be  welded 
either  to  itself  or  to  wrought  iron. 


32  XV. — METALLURGY. 


Kemarks. 

The  manufacture  of  the  weld  steels  and  of  crucible  steel  is 
losing  its  importance,  and  crucibles  are  now  principally  used 
for  small  masses  in  which  the  desired  quality  of  the  product 
can,  from  the  careful  supervision  exercised,  be  most  easily 
maintained. 

The  size  of  the  crucible  charge  depends  on  the  strength  of 
the  melter  and  rarely  exceeds  80  lbs. ;  but  with  well  drilled 
men  large  numbers  of  such  crucibles  may  be  poured  succes- 
sively into  a  common  ingot  mold  of  any  size.  Krupp  so  casts 
his  large  cannon,  sometimes  employing  1200  crucible  bearers. 

II.    IN    LARGE     MASSES. 

Processes. 

The  principal  processes  are  the  Bessemer  and  various  forms 
of  the  Open  Hearth.  Each  of  them  has  its  province.  The 
former,  owing  to  its  rapidity,  excels  in  cheapness,  although 
there  is  a  loss  of  about  10  per  cent,  of  iron  ;  the  latter,  owing 
to  its  controllability,  excels  in  quality.  This  takes  time  and 
increases  the  cost  by  about  15  per  cent.,  although  there  is  in- 
cidentally a  slight  gain  of  iron. 

Carbonization  and  Tests. 

Owing  to  the  loss  of  iron  from  oxidation  when  completely 
decarbonized,  neither  process  is  carried  to  an  extreme,  some 
C  being  always  left  in  the  metal  and  its  final  percentage  being 
regulated  by  adding  Sp  or  FM. 

The  percentage  of  C  is  judged  of  by  the  fracture ;  by  the 
appearance  of  the  nick  required  to  produce  fracture  ;  and 
more  carefully  by  a  rapid  color  test,  which  consists  in  compar- 
ing the  color  of  a  solution  of  the  metal  in  dilute  HNOg  with 
that  of  a  standard  solution.  In  the  Bessemer  process  this  in- 
formation is  applied  to  the  next  succeeding  heat ;  and  in  the 
Open  Hearth,  as  the  operation  is  less  hurried,  to  the  heat  itself. 

Temperature. 

The  high  temperature  attained  permits  re-melting  on  the 
spot  of  the  scrap  accumulating  in  all  steel  works,  which  would 


3tV.— MEtALLURGV.  33 


otherwise  be  of  little  value.  In  the  Bessemer  process  this  is 
due  to  the  oxidation  of  the  Si  in  the  pig ;  in  the  Open  Hearth 
to  the  Siemens  regenerator,  which  increases  the  temperature 
cumulatively  to  a  degree  limited  only  by  the  refractoriness  of 
the  furnace  linings  and  the  tendency  of  the  gases  to  disso- 
ciate. Thus,  like  many  other  inventions,  the  Open  Hearth 
process  had  to  wait  for  the  parallel  development  of  some  in- 
significant art,  i.  e.  that  of  the  brickmaker. 

Cranes. 

The  production  of  metal  by  both  processes  depends  upon 
the  facility  of  manoeuvring  large  masses.  Of  the  various  pat- 
terns of  cranes  used  for  this  purpose.  Sir  Wm.  Armstrong's 
hydraulic  crane,  or  some  modification  of  it,  is  especially  valu- 
able in  Bessemer  practice.  Its  efficiency  depends  upon  the 
arrangement  of  peculiar  valves  which  unite  at  a  central  point 
called  the  **  pulpit"  and  which  place  the  control  of  the  whole 
plant  in  the  hands  of  one  man. 

For  an  Open  Hearth  plant,  where  frequently  very  heavy 
masses  must  be  moved  and  where  the  operations  need  not  be 
so  rapidly  performed,  these  cranes  may  be  supplemented  by 
power  swinging  cranes  or  replaced  by  a  traveling  crane  cover- 
ing the  whole  building.  The  traveling  crane  consists  of  a 
horizontal  beam  the  ends  of  which  roll  on  raised  parallel 
tracks.  The  weight  hangs  from  a  truck  rolling  on  the  beam 
and  may  thus  be  transported  to  any  point  of  the  included 
volume.  This  crane  presents  many  advantages  and  is  used 
when  the  construction  of  the  plant  permits. 

Casting  Ingots. 

In  both  processes,  the  melted  steel  is  run  from  the  furnace 
into  a  ladle  from  which  it  is  distributed  by  a  crane  into  cast- 
iron  ingot  molds. 

Casting  is  sometimes  done  through  an  independent  iron 
gate  entering  the  mold  from  below  (Figure  24).  The  fluid 
metal  should  enter  in  a  quiet,  solid  stream  so  as  to  avoid 


84  XV. — METALLURGY. 


entangling  air.  This  is  best  done  by  emptying  the  ladle  into 
the  pool,  from  which  it  issues,  mider  a  constant  head,  through 
a  cylindrical  nozzle. 

For  gun  work,  the  ingots  are  like  Figure  25.  The  tong- 
hold  serves  to  attach  the  porter-bar  in  forging ;  and  the  drum, 
being  girt  with  a  sHng  chain,  permits  the  mass  to  be  moved 
about  and  turned  axially  under  the  hammer.  The  dotted 
lines  in  Figure  25  indicate  the  form  of  the  corresponding 
sections  of  the  ingot. 

Ingots  are  cast  at  as  low  a  temperature  as  possible  consist- 
ent with  fluidity  in  order  to  diminish  internal  strain  and  to 
save  the  inner  surface  of  the  mold,  injuries  to  which  may 
imprison  the  ingot. 

In  order  to  fill  the  voids  resulting  from  the  shrinkage  due 
to  internal  strains,  castings  of  all  kinds  are  generally  sur- 
mounted by  a  smkifig  head.  This  is  a  reservoir  of  the  melted 
metal,  the  cooling  of  which  is  often  retarded  by  containing  it 
in  a  relatively  non-conducting  mold. 

For  economy  of  fuel  it  is  generally  sought  to  forge  the  in- 
gots as  soon  as  possible  after  they  have  solidified  throughout  ; 
but,  owing  to  interruptions  in  the  work,  the  sequence  cannot 
always  be  maintained.  Ingots  may  thus  require  re-heating  ; 
this  should  be  gradual  so  as  to  avoid  internal  strain. 

Fluid  Compression. 

Whitworth's  method  of  fluid  compression  tends  to  obliter- 
erate  cavities  by  an  hydraulic  pressure  of  about  40000  lbs.  per 
square  inch.  A  very  strong  steel  mold  provided  with  a  por- 
ous lining  is  employed.  The  pressure  crushes  down  the  vesic- 
ulated  shell  first  formed  next  to  the  walls  of  the  mold,  and 
drives  the  fluid  metal  throughout  the  interstices.  The  lining 
allows  the  escape  of  gas.  By  this  means  the  ingot  is  reduced 
about  one  eighth  in  length  while  cooling  after  casting.  The 
best  results,  however,  are  thought  to  be  obtained  by  careful 
melting  and  after-treatment  of  the  steel  while  in  a  fluid  state. 


XV. — METALLURGY.  35 


Bessemer  Process. 

(Figures  27—30.) 

Varieties. 

There  are  two  general  processes  depending  on  the  nature 
of  the  pig-iron  converted.  If  free  from  P,  silicious  or  acid 
linings  may  be  used  ;  but  if  it  contains  much  P,  basic  linings 
are  required.  The  former  process,  which  is  the  more  com- 
mon, is  here  described. 

Metal. 

The  iron  must  contain  Si  as  a  fuel,  and  hence  gray  pig,  the 
color  of  which  is  due  to  the  carbon  displaced,  page  18,  is 
used.  It  should  be  free  from  P  and  S,  as  they  are  not  re- 
moved but,  owing  to  the  inevitable  loss  of  iron,  their  propor- 
tion is  increased. 

Main  Operation. 

The  pigs  are  usually  melted  in  a  cupola  and  the  fluid 
charge,  after  weighing,  run  into  the  converter.  A  blast  of 
air  is  then  blown  down  through  one  trunnion  and  up  through 
the  perforated  bottom  and  the  fluid  metal.  The  reactions 
resemble  those  of  puddling*  and  are  principally  due  to  the 
heat  evolved  by  the  burning  Si.  This  burns  out  the  Mn  and 
C  in  the  metal  and,  by  forming  ferreous  slags,  removes  part  of 
the  iron  also.  The  fluidity  of  the  metal  is  due  to  the  inten- 
sity of  the  heat ;  the  latter  is  due  to  the  rapidity  of  the  reac- 
tion consequent  upon  the  state  of  subdivision  of  the  mass. 
The  burning  Si  raises  the  temperature  and  promotes  the 
fluidity  of  the  bath  more  than  does  the  C,  because  the  CO 
formed  absorbs  much  heat  by  expansion  and  carries  it  off; 
the  slag  remains  and  protects  the  bath  from  cooling.  The 
small  portion  of  Mn  present  also  acts  as  a  fuel. 

The  basic  process  requires  the  blast  of  the  Bessemer  blower 


*  It  has  been  said  as  an  example  of  mechanical  progress,  that  we 
have  replaced  the  laborious  operation  of  the  puUdler's  rabHc  by  piercing 
the  iDolten  metal  by  invigjble  bars  of  air. 


?56  XV.— METALLURGY. 

to  be  prolonged  after  the  C  and  Si  in  the  pig  have  been  re- 
moved, the  burning  P  maintaining  the  fluidity  of  the  metal. 

Periods. 

Three  periods  are  recognized,  lasting  as  follows  : 

I.  Three  to  five  minutes,  Si  burning.  The  free  C  in  the 
pig  becomes  combined,  in  which  state  it  is  most  easily  oxi- 
dized.    The  flame  is  feeble,  with  a  hissing  noise. 

II.  Six  to  ten  minutes.  The  oxidation  of  C,  principally 
to  CO,  makes  the  mass  boil  with  a  thundering  noise.  A 
yellow  flame  of  incandescent  particles  is  emitted  at  the  nozzle. 

III.  Four  to  five  minutes.  The  flame,  principally  of  N,  is 
smaller,  and  of  a  pale  bluish  tint.  In  about  15  or  18  min- 
utes from  the  beginning,  the  flame  suddenly  drops,  showing 
that  the  C  is  almost  entirely  gone.  To  save  loss  of  iron  by 
further  oxidation,  the  blow  is  then  stopped  as  the  converter  is 
turned  down  ;  the  carbonizer  is  then  added  by  weight.  If 
Spiegel  is  used,  it  is  melted  in  a  separate  cupola. 

Final  Operations. 

The  carbonizer  preferred  for  low  steel  is  FM,  which,  al- 
though more  costly  than  Sp,  contains  less  C  in  proportion  to 
the  Mn,  so  that  enough  Mn  may  be  added  to  reduce  the  iron 
oxide,  combine  with  free  O,  and  impart  to  the  steel  its  char- 
acteristic qualities  without  introducing  enough  C  to  make  it 
unduly  hard.  The  production  of  FM  is  one  of  the  improve- 
ments for  which  this  application  of  the  process  had  to  wait. 

After  standing  for  a  few  minutes,  the  contents  of  the  con- 
verter are  poured  into  a  ladle,  the  slag  remaining  in  the  vessel; 
the  slag  is  then  emptied  and  the  vessel  turned  up  for  a  fresh 
charge. 

Remarks. 

The  melted  pig  may  be  conveyed  directly  from  the  blast  fur- 
nace ;  but  this  is  not  often  done,  as  it  prevents  the  prelimi- 
nary grading  of  the  pigs  by  fracture. 

The  process  is  principally  applied  to  the  manufacture  of 


XV. — METALLURGY.  37 


rails,  for  which  it  is  sufficiently  exact.  The  quaHty  of  the 
product  may  be  improved  if  time  and  waste  are  neglected  and 
the  process  carefully  watched  through  the  spectroscope. 

The  steps  of  the  operation  in  the  acid  and  the  basic  pro- 
cesses, showing  the  rates  at  which  the  solid  products  are 
oxidized  and  the  proportions  of  the  different  gases  succes- 
sively formed,  are  represented  in  figures  28,  29,  30.  In  each 
figure  one  scale  is  that  of  time  in  minutes  from  the  beginning 
of  the  blow,  and  the  other  represents  the  corresponding  per- 
centage of  the  special  product  in  question.  These  diagrams 
are  the  result  of  experiment. 

/  Open-Hearth  Process. 

Varieties. 

The  hearth  may  be  either  of  the  stationary  or  of  the  rotary 
type.  In  both  cases  the  advantages  of  the  process  depend 
upon  the  Siemens  regenerative  apparatus,  which  requires  a 
gaseous  fuel. 

The  rotary  hearth  has  the  advantage  of  steam  power  and 
of  facility  in  making  the  repairs  which  the  intense  heat  due 
to  the  regenerative  apparatus  frequently  requires.  It  is  also 
better  able  to  dephosphorize  pig-iron.  The  principal  objec- 
tion to  it  is  the  liability  of  derangement  of  the  rotating 
machinery ;  but  this  can  be  overcome.  Its  process  is  here- 
after described. 

Distinctions  were  formerly  made  between  the  "pig  and 
ore "  and  the  "  pig  and  scrap  "  processes,  depending  upon 
whether  the  melted  pig-iron  is  decarbonized  by  the  iron  oxide 
or  diluted  by  the  addition  of  scrap  steel  low  in  carbon. 
Such  distinctions  are  no  longer  important,  as  the  former  pro- 
cess is  generally  employed. 

The  Siemens  furnace  with  either  the  stationary  or  the  revolv- 
ing hearth  is  a  mighty  instrument  for  achieving  various  metal- 
lurgical  ends.    Accordingly,  many  combinations  are  made  in 


88  XV. — METALLURGY. 


its  employment,  pig-iron,  washed  pig,  ore,  fluxes,  and,  par- 
ticularly  for   commercial   products,   scrap   being   added   as 
required  or  convenient. 
Gaseous  Fuel. 

Advantages:  1st.  Controllability,  by  which  either  an  oxi- 
dizing, reducing,  or  neutral  flame  can  be  uniformly  obtained. 
2d.  Economy.  3d.  Cleanliness.  4th.  The  accuracy  with 
which  the  low  temperatures  used  in  annealing  ovens  may  be 
estimated  by  the  eye,  the  gas  having  been  temporarily  cut  off 
so  as  to  obtain  a  background  against  which  the  true  color  of 
Uhe  heated  piece  will  appear. 

The  gas  may  be  natural  or  artificial. 

Crude  petroleum  is  becoming  largely  used  as  a  fuel.  Being 
thrown  into  the  furnace  as  a  spray,  it  has  many  of  the  advan- 
tages of  a  gas.  It  is  also  converted  into  gas  by  the  action 
of  steam  at  a  high  temperature.* 

Siemens  Gas  Producer. 

This  consists  of  a  number  of  chambers  united  in  groups  of 
four  around  a  common  stack  E,  figure  31.  The  stacks  unite 
in  a  common  trunk  which  leads  with  a  slightly  downward 
inclination  to  the  valve  box  B  of  the  furnace,  figures  33,  34. 
Each  chamber  is  essentially  a  wedge-shaped  funnel  with  one 
inclined  side  terminating  at  the  bottom  in  a  grate  B  on  which 
the  fuel  is  slowly  burned.  The  CO^  formed,  ascending 
through  the  incandescent  mass,  becomes  2C0,  and,  with 
other  gases  due  to  the  partial  distillation  of  the  superin- 
cumbent fuel,  passes  through  the  flue  D  to  the  stack  E  and 
thence  to  the  trunk,  having  in  the  trunk  a  slight  excess  over 
atmospheric  pressure  to  prevent  leakage  inward.    The  increase 


*  The  oxygen  in  the  H^  O  combines  with  the  carbon  in  the  oil,  forming 
CO,  and  decomposing  the  hydro-carbons  into  new  compounds  richer  in 
H.  The  H  derived  from  the  steam  combines  with  the  new  compounds, 
and  makes  them  still  lower  in  the  paraffine  series.     (Bloxam,  Art,  320.) 


XV. — METALLURGY.  39 


of  density  due  to  cooling  causes  a  gradual  flow  along  the 
trunk.  The  same  effect  can  be  obtained  by  using  a  blast 
which  gives  more,  better  and  hotter  gas  from  fewer  producers 
burning  poorer  fuel  than  does  the  natural  draft  described. 

Almost  any  kind  of  fuel  from  gas  coal  to  sawdust  may  be 
used,  depending  on  the  purpose  in  view. 

The  charging  hopper  A  and  the  poker  hole  Care  stopped 
to  prevent  the  escape  of  gas. 

.  Siemens  Stationary  Furnace. 

(Figures32,  33,  34.) 

Hearth. 

This  rests  in  a  cast-iron  basin  T,  beneath  and  around  which 
air  circulates.  It  is  enclosed  in  a  rectangular  box-like  fur- 
nace about  30  feet  long,  standing  above  the  floor-line  W,  and 
provided  with  the  charging  door  U,  and  the  spout  V  iox  tap- 
ping out  the  fluid  charge. 

Regenerators. 

These  are  the  essential  parts  of  the  apparatus  and  are 
applied  to  many  purposes  in  which  high  temperatures  are 
required. 

The  regenerator  consists  of  four  fire-brick  chambers  of 
varying  section,  K;  L ;  M;  iV,  arranged  in  pairs.  They 
are  filled  with  a  crib  work  of  loosely  stacked  fire-brick.  From 
each  of  the  end  chambers  K^  JV,  gas-flues  S  lead  up  into  the 
furnace ;  and  from  each  chamber  Z,  M,  three  air-flues  P  and 
R  lead  up  alongside  the  gas-flues  to  a  point  above  their  exit 
in  the  furnace.  This  arrangement  protects  the  metal  from 
oxidation  ;  and  the  roof,  made  higher  than  where  reverbera- 
tion is  sought,  from  erosion  by  the  flame. 

Valves, 

The  gas,  air,  and  reversing  valves  are  shown  in  vertical  sec- 
tion (laid  over  a  longitudinal  section  of  the  regenerators)  in 
Figure  32 ;  in  plan  (laid  over  a  horizontal  section  of  the  main 


40  XV. — METALLURGY. 


flues)  F,  G;  Jy  H  in  Figure  34 ;    and  in  cross  section  in 
Figure  33. 

Operation. 

Gas  from  the  producers,  regulated  by  the  valve  B,  passes 
down  over  the  reversing  valve  C ;  this  is  set  so  as  to  direct 
the  gas  into  the  main  flue  F  and  the  regenerator  K,  where  it 
percolates  through  the  mass  of  hot  brickwork  and  thence 
passes  at  a  high  temperature  into  the  furnace.  Air  is  drawn 
through  the  regulating  valve  F  over  the  reversing  valve  C , 
through  the  main  flue  G  into  the  hot  regenerator  L  and, 
passing  up  the  flue  /*,  meets  the  hot  gas  as  above  described, 
affording  progressive  combustion  with  intense  heat. 

After  burning,  the  flame  passes  down  the  flues  R^  S  into 
the  other  pair  of  regenerators  J/,  N^  which  absorb  most  of 
its  heat.  It  then  escapes  through  the  main  flues  J,  H  under 
the  two  reversing  valves,  and  into  the  chimney  flue  AA' . 

After  about  twenty  minutes,  K,  L  becoming  cooler  and  M, 
N  heated,  C,  C  are  reversed  by  the  handles  D,  when  the 
currents  of  gas  and  air  are  also  reversed.  The  efl"ect  of 
reversal  is  cumulative,  since  to  the  heat  of  combustion  is 
added  that  which  the  gases  absorb  from  the  brickwork  before 
combustion.  As  the  brickwork  becomes  progressively  hotter, 
the  ultimate  temperature  attainable  is  independent  of  blast  or 
draught  and  is  limited  only  by  the  refractoriness  of  the  furnace 
linings  and  the  tendency  of  the  gas  to  dissociate  at  high  tem- 
peratures. 

Advantages. 

The  principal  advantages  are  the  high  and  uniform  tem- 
peratures attainable,  with  the  other  advantages  due  to  the  use 
of  gaseous  fuel. 

Employment. 

When  the  furnace  has  been  brought  up  to  a  melting  heat, 
the  bottom  is  repaired  with  fire-sand  and  the  charge  thrown 


XV. — METALLURGY.  41 


in  by  hand.     After  melting,  it  is  stirred  with  iron  -bars  and 
treated  as  hereafter  described  in  the  Rotary  Hearth, 

Pernot  Rotary  Hearth. 

(Figure  35.) 

Hearth. 

This  consists  essentially  of  a  circular  wrought-iron  '  ^ pan  " 
lined  with  refractory  material  and  mounted  on  conical  rollers. 
These  run  on  a  circular  trough-shaped  track  mounted  on  a 
carriage  ;  the  latter  rolls  on  two  parallel  rails  on  which  it  may 
be  run  into  and  out  of  the  stationary  furnace  chamber.  The 
pan  is  rotated  by  a  circular-toothed  rack  beneath  it  gearing 
into  a  toothed  wheel  or  by  an  endless  screw  driven  by  steam 
power.  The  pintle,  which  is  hollow  and  contains  a  stream 
of  water,  is  incHned  at  about  6°,  so  as  to  bring  the  highest 
portion  of  the  hearth  next  to  the  door.  In  case  of  accident 
to  the  tapping  hole,  more  than  one  is  provided. 

The  lining  of  the  pan  varies  with  the  kind  of  work.  For 
ordinary  melting  it  is  of  refractory  siUcious  material;  but 
where  dephosphorization  is  sought  by  the  Krupp  process,  the 
lining  is  basic,  preferably  of  lumps  of  refractory  magnetite 
set  in  a  paste  made  of  powdered  haematite  and  iron  scale. 
The  lower  courses  of  the  roof  are  then  of  dolomite  brick. 

Operation 

For  steel  making,  the  charge,  consisting  of  about  15  tons 
of  pig-iron  free  from  P  and  6",  is  thrown  in  through  the  charg- 
ing door  while  the  pan  is  revolving ;  this  distributes  it  auto- 
matically. Further  revolution  of  the  pan  then  causes  the 
unmelted  metal  to  dip  into  and  out  of  the  bath  as  previously 
described  for  wrought  iron.  When  the  pig-iron  is  thoroughly 
melted,  rotation  is  stopped  and  ore  is  added  at  intervals, 
each  addition  being  followed  by  a  violent  ebullition  of  the 
bath.  Samples  of  metal  or  ''spoon  tests'*  are  taken  from 
time  to  time  and  examined  by  the  color  test,  the  fracture,  and 


42  XV. — METALLURGY. 


by  the  appearance  of  the  nick  made  by  the  chisel  at  the 
fracture.  When  the  C  in  the  bath  is  low  enough,  Si  and  Mn 
are  added  to  prevent  vesiculation  and  to  make  the  steel 
malleable.  The  process  is  continuous,  taking  about  eight 
hours  for  a  heat,  with  a  variable  interval  for  repairs. 

Bepairs. 

The  hearth  is  repaired  between  heats  by  revolving  it  so  as 
to  bring  the  portions  most  cut  by  the  flame  under  a  hole  in 
the  roof  through  which  material  is  thrown.  The  stationary 
portion  is  repaired  at  about  every  twenty  heats,  the  pan  being 
run  out  bodily  on  its  carriage.  This  afl"ords  a  considerable 
advantage,  since  in  repairing  the  stationary  furnace,  time  must 
be  taken  to  allow  the  mass  of  brickwork  to  cool  down  to  an 
endurable  temperature ;  owing  to  the  lack  of  ventilation  this 
time  may  be  very  great. 


V.  MECHANICAL  TREATMENT  OF  STEEL. 

CASTING. 

The  successful  casting  of  steel  into  final  forms  is  still  un- 
certain. The  principal  difficulties  arise  from  vesiculation  and 
internal  strain  Steel  castings  frequently  replace  iron  forg- 
ings  of  a  low  grade. 

ROLLING 

Rolling  may  be  intended  to  produce  forms  either  straight 
or  circular,  and  may  be  performed  either  hot  or  cold.  The 
latter  has  the  special  object  of  producing  hard,  polished  sur- 
faces of  exact  dimensions  and  is  applied  to  iron  or  steel  of 
small  sections  only.     The  reduction  is  small. 

Hot  Rolling— Straight. 

The  following  description  of  the  rolHng  of  armor  plate  or 
of  structural  steel  is  taken  as  a  type. 

The  interior  of  a  newly  cast  ingot  is  too  liquid  for  safe 


XV. — METALLURGY.  43 


working,  and  by  the  time  that  this  has  sufficiently  cooled  in 
the  air,  the  exterior  has  become  too  hard.  Consequently, 
the  cooling  is  often  retarded  in  non-conducting  soaking  pits, 
in  which  the  initial  heat  of  the  interior  and  that  which  be- 
comes sensible  during  solidification  become  uniformly  dis- 
tributed throughout  the  mass. 

Or,  if  the  ingot  has  become  cold,  it  is  brought  slowly  to 
the  proper  temperature  in  a  heating  furnace.  If  this  is  done 
too  rapidly,  the  exterior  may  be  over-heated  before  the  interior 
is  at  the  proper  temperature.  The  principle  involved  is  of 
wide  application  in  the  treatment  of  steel. 

The  universal  mill  consists  of  two  pairs  of  massive  rolls  at 
right  angles  to  each  other,  so  that  one  pair  will  roll  the  sides 
of  the  ingot  while  the  other  pair  rolls  its  top  and  bottom. 
Each  pair  is  driven  by  an  independent  steam  engine.  The 
direction  of  the  rotation  may  be  rapidly  reversed,  and  the 
space  between  the  members  of  each  pair  of  rolls  be  rapidly 
adjusted  to  suit  the  varying  dimensions  of  the  work. 

A  series  of  horizontal  parallel  rollers  of  small  diameter, 
independently  driven,  convey  the  ingot  to  and  from  the  rolls, 
and  after  rolling  take  it  to  the  shears  where  it  is  trimmed  and 
cut  into  lengths. 

These  lengths,  or  blooms^  are  often  re-heated  and  re-rolled 
by  a  mill  trai?i  into  various  structural  shapes.  For  small  work 
the  mill  train  usually  consists  of  a  series  of  rolls  arranged  in 
sets  of  three,  one  above  the  other,  or  three  high.  They  con- 
tain grooves  of  appropriately  decreasing  section  so  that  suc- 
cessive/^i^i'<fi'  reduce  the  bloom  to  the  shape  required.  The 
rotation  of  each  roll  is  continuous,  so  that  the  piece  passes 
in  one  direction  above  the  middle  roll,  and  in  the  opposite 
direction  beneath  it. 

In  roUing  large  sections  the  two-high  system  is  generally 
employed ;  the  rotation  being  reversed  and  the  space  adjusted 
at  every  pass. 


44  5tV.— MEtALLURGY. 


In  all  large  forgings  great  care  is  taken  to  cut  out  all  visible 
imperfections  such  as  pulls^  which  arise  from  deficient  duc- 
tiHty  in  the  metal,  and  cold  shuts,  whicli  are  due  to  the  folding 
in  of  projecting  portions  at  temperatures  too  low  to  admit  of 
their  union  to  the  mass. 

Hot  Rolling  —  Circular. 

A  small  cylindrical  ingot  is  flattened  out  or  "  upset "  into  a 
"cheese"  and  punched  from  each  side  successively  with  a 
conical  drift.  The  punchings,  or  pieces  cut  out,  usually  con- 
tain all  the  pipe.  It  is  afterward  hammered  on  the  horn  of 
an  anvil,  figure  37,  until  the  approximate  forjji  is  obtained. 
Then,  being  hung  upon  a  fixed  roller  A,  figure  38,  another 
roller  B,  independently  driven  at  a  higher  rate  of  speed,  is 
raised  by  hydraulic  pressure  to  the  position  shown  by  the 
dotted  lines.  The  thickness  of  the  hoop  is  thus  diminished, 
and  its  diameter  increased,  since  lateral  spread  is  prevented 
by  the  flanges  a  b  which  come  in  contact,  each  with  the  end 
of  the  other  roller.  The  process  is  used  for  making  locomo- 
tive tires  and  short  hoops  for  guns.  It  tends  to  give  a  fibrous 
structure  to  the  steel,  aff"ording  great  tangential  strength. 

WIRE    DRAWING. 

Operation. 

This  resembles  rolling,  except  that  the  conical  aperture  in 
the  draw  plate,  figure  39,  being  stationary,  the  wire,  previously 
pointed  and  lubricated,  is  drawn  through  it  by  power,  gener- 
ally by  being  coiled  around  a  revolving  drum.  Tubing  is 
similarly  made,  but  large  sizes,  like  gun-barrels,  are  rolkd  as 
described  for  rails,  the  sides  being  kept  apart  by  an  axial 
mandrel  which  is  stationary. 

Effects. 

The  effect  of  wire  drawing  at  low  temperatures  resembles 
that  of  cold  rolling  in  that  it  raises  the  elastic  limit  and  tenacity 


XV. — METALLURGY.  45 


and  diminishes  the  ductility  of  the  metal  so  much  that,  if  the 
original  section  is  much  reduced,  frequent  annealing  is  nec- 
essary. Steel  wire  has  thus  been  given  a  tenacity  of  over 
333,000  lbs.  per  square  inch  with  an  elastic  limit  half  as  high. 
These  qualities  are  especially  adapted  to  the  construction  of 
"  wire-wound"  cannon. 

FORGING. 

This  includes  the  operations  by  which  hot  metal  is  ham- 
mered into  shape.  It  therefore  requires  furnaces,  hammers 
and  anvils. 

Furnaces. 

For  large  masses  modifications  of  the  Siemens  fupnace 
called  re-heating  furnaces  are  now  employed.  These  furnaces 
are  frequently  served  by  a  curved  crane  of  the  form  shown  in 
figure  42.  This  increases  the  elasticity  of  the  crane  as  against 
the  shocks  due  to  forging. 

Hammers. 

For  light  work  hammers  may  be  of  the  vibrating  class  known 
as  ////  or  helve  hammers,  figure  40,  in  which  a  horizontal  beam, 
working  on  trunnions,  carries  at  one  end  a  heavy  head  ;  this 
is  caused  to  rise  and  fall  by  the  action  of  projections  on  a  re- 
volving wheel.  Or  they  may  be  of  the  class  known  as  drop 
hammers,  where  a  weight  is  raised  by  hand  or  by  power  and 
allowed  to  fall  upon  the  work  after  the  manner  of  a  pile 
driver,  figure  41. 

But  for  heavy  work  steam  hammers  are  used.  They  are 
sometimes  of  the  Single  Acting  type,  figure  42,  proposed  by 
Nasmyth  in  1833.  The  inverted  cylinder  is  mounted  on  legs 
which  spread  sufficiently  to  allow  freedom  for  the  workmen. 
The  cylinder  is  usually  traversed  vertically  by  a  heavy 
piston-rod,  to  the  lower  end  of  which,  sliding  in  guides 
attached  to  the  frame,  is  fastened  a  heavy  head  or  tup. 
Steam  being  admitted  below  the  piston,  it  raises  the  hammer, 


46  XV. — METALLURGY. 


which  is  allowed  to  fall  from  any  desired  height.    Its  fall  may- 
be arrested  by  choking  the  exhaust  by  the  automatic  opera- 
tion of  the  valves  so  that  rapid    rebounding  blows  may  be 
struck.     See  figure  43  and  page  54. 
Anvils. 

The  anvil  with  its  foundations  constitutes  one  of  the  most 
expensive  portions  of  a  forge  plant.  The  anvil  of  the  125- 
ton  hammer  at  South  Bethlehem,  Pa.,  copied  from  that  shown 
in  figure  42,  weighs  about  1600  tons. 

In  order  to  avoid  the  effects  of  vibration,  the  foundations 
of  the  anvil  should  be  independent  from  those  of  the  hammer. 

The  anvil  proper,  like  the  tup,  is  generally  flat,  but  both 
may  be  of  various  forms  required  by  the  shape  of  the  work. 
Small  work  is  thus  produced  with  great  exactness  by  being 
stamped  between  dies.  The  parts  of  small-arms  and  of  other 
machines  made  in  great  quantities,  such  as  those  for  sewing 
and  for  agricultural  purposes,  are  thus  very  economically 
forged  into  very  nearly  their  finished  sizes.  When  of  hori- 
zontally rectangular  section,  the  anvil  is  generally  set  with  one 
of  its  diagonals  in  the  plane  of  the  legs,  so  as  to  give  room 
opposite  all  its  faces  for  handling  long  forgings.     Figure  43. 

The  energy  on  impact  being  the  same,  the  action  of  a  heavy 
weight  moving  with  a  low  velocity  is  preferred,  as  the  efi"ect 
is  more  penetrating  and  less  local.  This  principle  is  utilized 
in  Condies  hammer,  in  which,  owing  to  the  fact  that  the  mass 
of  the  cylinder  is  necessarily  greater  than  that  of  the  piston- 
rod,  the  cylinder  is  made  movable,  the  piston-rod  being  sta- 
tionary. 

The  steam  may  be  admitted  above  the  piston,  adding  its 
pressure  to  the  weight  of  the  moving  mass.  Such  hammers 
are  Double  Acting. 

For  small  work  a  single  support,  figure  43,  gives  sufficient 
steadiness  and  more  room.  The  valve  may  then  be  worked 
by  a  treadle  under  the  control  of  the  smith  so  as  to  give  him 
the  use  of  both  his  hands.     See  figure  41. 


XV. METALLURGY.  47 


The  local  absorption  of  energy  at  the  point  of  impact  di- 
minishes the  reaction  of  the  anvil,  so  that,  as  the  thickness 
of  the  work  increases,  the  thoroughness  of  the  forging  dimin- 
ishes. This  requires  frequent  rotation  of  the  work  so  that  all 
sides  may  be  equally  extended.* 

For  this  reason  Ramsbottam's  duplex  hammer  is  used,  the 
work  lying  between  horizontal  hammers  moving  with  equal 
and  reciprocal  velocities. 

Anvils  for  hollow  work.  In  forging  hollow  work,  mandrels, 
which  are  heavy  solid  cylinders  passed  through  the  forging, 
are  used  in  connection  with  the  anvil  proper.  If  supported 
throughout  its  length  by  a  V-shaped  notch  in  the  anvil,  the 
forging  lymg  in  between,  the  mandrel  is  termed  _/fj:^^/  if  sup- 
ported only  and  directly  at  its  ends,  the  mandrel  is  called 
swinging.     Figures  44,  45. 

The  effect  of  forging  is  greatly  affected  by  the  way  in  which 
the  mandrel  is  used.  Forging  on  a  fixed  mandrel  extends 
the  work  in  length  but  does  not  sensibly  affect  the  internal 
diameter.  Forging  on  a  swinging  mandrel  increases  both 
internal  and  external  diameters  without  affecting  the  length 
of  the  work.  Hence,  the  swinging  mandrel  is  used  for  hoops 
which  are  too  wide  for  the  tire-rolling  machine. 

Forging  Press. 

The  defects  in  steam  hammers  above  referred  to  will  prob- 
ably lead  in  time  to  a  more  general  use  of  the  hydraulic  forging 
press  designed  by  Whitworth,  Figures  44,  45.  Its  principal 
advantage  lies  in  the  time  during  which  the  work  is  operated 
on;  this  permits  the  molecular  flow  desired. t 

*  This  is  also  true  of  rolling  and  limits  the  effective  thickness  of  armor 
plates. 

t  Opinions  are  divided  as  to  the  comparative  merits  of  the  hammer  and 
the  press.  The  advocates  of  the  hammer  prefer  it  on  the  following  grounds  : 

1.  In  forging  solid  work  the  effect  of  the  hammer  is  greatest  on  the 
exterior  which  is  retained;  and  least  on  the  interior,  which  for  cannon 
and  heavy  shafting  is  subsequently  removed.  The  converse  of  this  is 
attributed  to  the  press. 


48 


XV. METALLURGY. 


VI.  MOLECULAR  TREATMENT  OF  STEEL. 

The  quality  of  steel  depends  upon : 

1.  Its  composition. 

2.  Its  structure  as  modified  by  heating  and  cooling. 

1.  Composition. 

Pure  iron  and  carbon  make  a  typical  steel.  But  other  ele- 
ments are  of  necessity  present  in  all  the  steels  met  with  in 
practice. 

Pure  carbon  steel  is  here  discussed. 

2.  Structure. 

Changes  in  structure  from  the  effects  of  heating  and  quench- 
ing steel  appear  to  be  associated  with  changes  in  its  density 
and  also  in  the  state  of  the  contained  carbon.  What  relation 
exists  between  the  change  in  state  of  the  carbon  and  the 
change  in  the  structure  of  the  steel  is  still  uncertain. 

States  of  Carbo7i. 

Indeed,  the  precise  nature  of  the  states  of  the  carbon, 
although  much  experimented  upon  and  discussed,  is  not 
definitely  known.  As  an  indication  of  the  uncertainty  in 
this  matter,  and  also  of  the  idea  which  most  theories  contain, 
the  following  suppositions  may  be  referred  to. 

The  carbon  is  supposed  by  Professor  Abel  to  be  either  in 
the  condition  of  an  alloy,  or  of  a  diffused  carbide.  Another 
chemist  calls  it  diamond,  or  dissolved  carbon.  Others,  and 
the  more  recent  authorities,  waive  this  issue  by  calling  it 
**  hardening  "  or  "  cement"  carbon.     See  page  18. 

Avoiding  any  specific  hypothesis,  we  may  designate  these 
states  respectively  as  Fixed  or  Free,      The  former  name,  as 

2.  The  prolonged  contact  with  the  dies  of  the  press  chills  the  forging, 
the  initial  temperature  of  which  therefore  must  be  excessive ;  while  the 
blows  of  the  hammer  are  heating. 

3.  Hammering  exposes  superficial  defects  while  pressing  conceals  them. 
The  1 25-ton  hammer,  page  46,   is  intended  for  forging  armor  plates, 

the  quality  of  the  surface  of  which  is  most  important. 


3tV.— METALLURGY.  49 


the  preceding  nomenclature  would  indicate,  corresponds  to 
the  hard  condition  of  steel,  resembling  that  of  white  cast  iron ; 
and  the  latter  to  its  softer  condition,  resembling  gray  iron. 
See  Bloxam,  middle  Art.  220. 

BrinelVs  Experiments, 
Method. 

The  accompanying  diagrams,  Figure  46,  are  principally 
based  upon  a  long  series  of  experiments  made  by  a  Swedish 
engineer,  J.  A.  Brinell,  upon  the  changes  in  the  structure  of 
steel  due  to  heating  it  in  diiferent  temperatures  and  cooling  it 
at  different  rates.  His  results  appear  to  agree  well  with  those 
of  others.     His  method  was  : 

I.  To  heat  separate  bars  of  the  same  steel,  but  of  varying 
structure,  up  to  certain  temperatures  indicated  by  the  color 
of  the  hot  metal,*  and  then  to  cool  them  in  one  of  two  ways  : 

1.  Slowly  in  ashes,  called  herein  cooling. 

2.  Suddenly  in  cold  water,  called  herein  quenching. 

n.  To  examine  a  freshly  fractured  surface,  the  fracture 
being  similarly  produced  in  all  cases. 

HI.  To  subject  the  steel  after  cooling  or  quenching  to  a 
chemical  test  as  to  the  state  of  the  carbon  contained. 

Classification  of  Fractures. 

The  recognition  of  fractures,  like  that  of  colors  due  to  cer- 
tain temperatures,  requires  great  experience,  but  the  principal 
fractures  may  be  designated  by  symbols,  as  follows  ; 

Structure.  Crystalline.  Granular. 

i  Coarse,  A.  D. 

Symbols.  \  Intermediate,  B.  E. 

(  Finest,  C.  F. 

Aspect,  glistening,  dull. 

The  most  important  is  F,  which  may  be  called  amorphous^ 


*The  irisated  colors  in  figure  46  are  the  chameleon  tints  of  the 
films  of  iron  oxide  of  different  thickness,  which  result  when  a 
polished  steel  surface  is  moderately  heated. 


50  XV.— METALLURGY. 


the  crystals  or  grains  being  invisible  to  the  naked  eye.  The 
intermediate  and  various  composite  fractures  described  by 
Brinell  are  not  noted  herein. 

Characteristics  of  Fractures. 

A,  B,  C,  are  relatively  soft. 
D,  E,  F,  are  relatively  hard. 
A,  D,  have  low  density  (open  grain)  and  are  weak. 
C,  F,  have  high  density  (close  grain)  and  are  strong. 
Therefore,   C  has  softness  and  strength ;  it  is  extensible. 
This  fracture  is  sought  in  annealing. 

Therefore,  F  has  hardness  and  strength  ;  it  is  inextensible. 
This  fracture  is  sought  in  hardening. 
F  has  the  maximum  density. 

DIAGRAMS. 

Explanation. 

Figure  46  illustrates  the  changes  in  structure  and  state  due 
to  heating  and  either  cooling  or  quenching  the  steel  experi- 
mented on  by  Brinell.  The  axis  of  each  diagram  intersects  a 
common  scale  of  temperatures  which,  for  any  particular  grade 
of  steel,  are  indicated  by  the  accompanying  colors. 

The  temperature  W  is  critical  in  its  effects  on  structure  and 
state :  it  is  the  only  high  temperature  at  which,  without  having 
been  exceeded,  if  steel  be  que7iched,  the  resulting  fracture  will  be 
amorphous,  F.  The  lower  the  grade  of  steel,  the  higher  is  the 
temperature  corresponding  to  F,  and  conversely.  The  cor- 
responding color  must  be  determined  empirically  for  each 
grade,  and,  for  important  work,  even  for  each  ingot  of  steel. 

The  steel  used  by  Brinell  had  about  0.50  per  cent,  carbon, 
such  as  is  used  for  cannon. 

Each  diagram  represents  a  group  of  experiments  upon  bars 
in  which  the  same  structure  had  been  previously  produced  by 
the  methods  indicated  above.  An  ordinate  along  the  axis 
represents  the  temperature  to  which  a  piece  of  steel  was 
heated  ;  the  abscissa  to  the  left  represents  roughly  the  result- 


XV. — METALLURGY.  51 

ing  coarseness  of  structure.  The  character  of  the  structure  is 
indicated  by  reference  letters.  The  extremities  of  abscissae 
so  determined  are  connected  by  a  line  indicating  whether, 
after  heating  to  the  desired  extent,  the  bars  were  quenched  or 
cooled. 

'Quenching  is  represented  by  a  full  line . 

Cooling  is  represented  by  a  wavy  line'-^^_^'^,^_^'^.^^  . 

The  dotted  line  to  the  right  of  the  axis  represents  roughly 
by  its  abscissae  the  state  of  the  carbon  at  different  temperatures, 
its  relative  freedom  being  represented  by  the  corresponding 
abscissae  of  the  dotted  hne. 

Interpretation. 

Study  of  the  diagrams  will  show  that — • 

At  W  quenching  always  gives  F  and  fixes  carbon. 

At  W  cooling  always  gives  C  and  frees  carbon. 

Below  W  the  crystalline  structure  does  not  change. 

Below  W  the  granular  structure  gradually  becomes  finer. 

Below  W  the  amorphous  structure  gradually  becomes 
coarser  (the  only  change  possible). 

Above  W  all  structures  gradually  become  coarser,  being 
crystalline  if  cooled,  and  granular  if  quenched. 

The  change  of  carbon  from  free  to  fixed  is  sudden  and  is 
called  hardening. 

The  change  of  carbon  from  fixed  to  free  is  gradual.  If 
partial,  it  is  called  tempering,  and  if  total,  it  is  properly 
termed  annealing. 

Crystalline  structure  is  associated  with  free  carbon. 

Granular  structure  is  associated  with  fixed  carbon. 

Conclusions  as  to  the  Treatment  of  Steel. 

1.  After  forging  a  cutting  instrument  or  spring,  it  must  be 
hardened  so  as  to  fix  the  carbon,  as  a  necessary  preliminary 
to  its  gradual  release  by  tempering. 

2.  In  tempering  hardened  steel,  the  less  it  is  heated  the  less 


52  XV. — METALLURGY. 


is  its  structure  affected;  and  the  less  is  the  change  in  the 
state  of  the  carbon. 

8.  The  fixed  state  is  the  more  stable,  so  that  it  takes  time 
to  change  it  throughout  the  mass  without  exceeding  the  de- 
sired temperature  externally.  Such  an  excess  would  affect 
the  structure  of  the  over-heated  parts.  The  metallurgical 
term  soaking  aptly  illustrates  the  manner  of  heating  steel 
from  which  the  best  results  are  obtained. 

The  effects  due  to  a  given  temperature  may,  however,  be 
produced  by  exposing  the  steel  to  a  lower  temperature  for  a 
longer  time  than  usual.  Many  of  the  following  apparent 
exceptions  to  the  general  rules  appear  to  depend  upon  the 
question  of  time. 

4.  The  carbon  having  been  freed  by  slow  heating,  the  rate 
of  the  cooHng  below  W  is  indifferent  unless  the  mass  of  the 
piece  be  so  great  as  to  cause  the  structure  to  change  from  the 
prolonged  action  of  its  internal  heat. 

5.  If  W  be  exceeded  the  effect  on  structure  of  hardening  is 
lost,  and  the  steel  must  be  cooled  below  W  and  re-heated  to 
W  to  refine  it. 

Use  of  the  Term,  Temper. 

Much  confusion  has  followed  the  loose  use  of  the  term 
temper.  Besides  being  applied  to  the  grade  of  steel,  it  is  also 
commonly  used  to  indicate  hardening;  whereas  we  see  that — 

Hardening  is  produced  by  quenching  at  W  and  fixing  the 
carbon. 

Tempering  is  a  mitigation  of  the  hardness  above  produced 
which  follows  from  subsequently  heating  steel  to  some  tem- 
perature below  W,  the  proportion  of  the  carbon  thus  freed 
depending  on  the  temperature  attained.  Whether  the  steel 
should  then  be  cooled  or  quenched  depends  upon  the  mass 
of  the  piece.     It  is  usually  quenched. 

Annealing  properly  consists  in  cooling  at  W  so  as  to  free 
all  the  carbon  possible  and  to  destroy  the  effects  of  harden- 


X'V. — METALLURGY.  58 


ing.  But  it  is  also  a  term  commonly  applied  to  the  cooling 
below  W  of  steel,  whether  previously  fully  hardened  or  not. 
According  to  the  temperature  attained  and  to  the  time  taken 
to  cool  the  piece,  it  is  softened  and  freed  from  internal 
strain. 

Bate  of  Cooling. 

The  brittleness  and  the  hardness  of  steel  will  be  increased 
by  increasing  the  rate  of  cooling  from  W,  either  by  quench- 
ing in  mercury,  or  in  water  the  conductivity  of  which  has 
been  increased  by  acidulation  or  by  the  solution  of  a  salt. 
The  same  effect  is  obtained  by  using  water  at  a  low  temper- 
ature, or  by  frequent  changes  of  the  particles  in  contact,  by 
motion  either  of  the  metal  or  of  the  water. 

By  reducing  the  rate  of  cooling  as  by  the  use  of  oil  or 
tallow,  the  effect  known  as  oil  hardening  is  produced.  Its 
effect  is  intermediate  between  C  and  F,  and  is  probably  largely 
mechanical,  the  sudden  cooling  of  the  external  layers  prevent- 
ing the  expansion  of  the  internal  mass  during  subsequent 
attempts  at  crystallization.  This  limits  the  size  of  the  crystals 
formed  and  increases  the  strength  of  the  metal;  but  it  pro- 
duces some  internal  strain  which  may  be  relieved  by  temper- 
ing at  a  low  heat.  The  charred  oil  next  to  the  surface,  like 
the  scale,  tends  to  delay  cooling. 

EFFECTS  OF  FORGING, 

Above  W. 

Except  when  in  small  masses  steel  is  generally  heated  above 
W  in  order  to  give  it  the  plasticity  required  for  forging.  In 
this  case  the  crystals  are  not  supposed  to  be  destroyed  but  to 
be  softened  and  expanded  by  the  heat.  Having  been  further 
disturbed  by  the  hammer,  they  are  supposed  on  cooling  to 
assume  the  sizes  and  shapes  due  to  the  temperature  at  which 
they  have  been  worked,  with  intervals  between  the  crystals 
depending  on  the  treatment  received.  Free  crystallization 
thus  implies  porosity  and  a  diminished  density,  which  is 
further  diminished  by  heavy  forging  at  a  high  heat. 


M  XV. — METALLURGY. 


Owing  to  the  tendency  of  the  crystals  to  shde  over  their  ad- 
jacent surfaces,  a  heavy  blow  may  cause  the  fracture  of  over- 
heated steel.  It  may  indeed  fall  to  pieces  in  the  fire.  But, 
if  such  steel  be  lightly  and  rapidly  hammered  over  its  entire 
surface,  the  effect  will  resemble  that  due  to  agitating  a  crystal- 
lizing solution  (Bloxam,  Art.  38),  m  the  reduction  of  the  size 
of  the  crystals  and  in  the  increased  strength  of  the  material. 

This  effect  having  been  attained,  further  forging  at  a  lower 
temperature  tends  to  form  the  piece  and  to  distribute  locally 
any  cavities  which  may  exist. 

In  forging  gun  work  the  ingot  is  reduced  in  thickness  about 
one-half;  the  reduction  being  greatest  for  those  portions  of 
the  gun  that  lie  nearest  to  the  bore. 

Wa/er  Annealing.  Owing  to  the  difficulty  of  penetrating 
large  masses  of  metal  by  the  vibrations  of  the  hammer,  the 
greater  part  of  the  metal  treated  as  above  will  be,  when  cooled, 
like  A  or  B  or  a  combination  of  both.  When  the  size  of  the 
piece  permits,  one  remedy  proposed  is  to  re-heat  slowly  to  W, 
to  quench  so  as  to  prevent  free  crystaUization,  and,  as  soon 
as  the  temperature  falls  sufficiently  below  W,  to  remove  the 
steel  from  the  water  and  allow  it  to  cool  slowly  in  air.  See 
Diagrams  IV  and  V.  The  internal  heat  removes  internal 
strain.  Railway  axles  are  thus  treated,  the  process  being 
called  "water  anneaUng." 

The  structure  of  a  steel  casting  may  be  improved  by  heat- 
ing it  to  W  and  cooling  it  slowly. 

Forging  Below  W. 

When  the  hammer  is  of  sufficient  power,  the  best  effect  will 
be  attained  by  forging  just  below  W.  The  crystals  are  sup- 
posed not  to  be  much  expanded  by  this  heat ;  but,  being 
softened,  they  may  be  compacted  so  as  to  destroy  the  porosity 
due  to  free  crystallization.  This  treatment  gives  the  highest 
density  attainable,  viz.,  8.0;  the  steel  resists  the  file,  has  a 


XV. — METALLURGY.  6B 


waxy  fracture,  and  yields  a  beautifully  veined  surface  when 
etched.*  This  work  requires  hammers  of  great  power  when 
large  masses  are  thus  forged. 

The  experience  of  all  steel  makers  tends  to  show  the  ad- 
vantage of  forging  at  as  low  a  temperature  as  possible.  Work- 
men incline  to  over- heat  the  steel  so  as  to  diminish  their  labor, 
— but  this  should  be  avoided. 

A  very  fine  quality  of  steel  wire  made  in  England  by  Stubbs 
and  much  used  for  making  drills  and  fine  tools  is  said  to  be 
made  by  being  forged  between  semi-cylindrical  dies  by  a  light 
"pony"  trip-hammer  running  with  very  great  rapidity.  The 
temperature  required  is  attained  by  the  hammering. 

INTERNAL  STRAINS. 

These  arise  from  differences  in  the  rate  of  cooling  through- 
out the  mass,  being  increased  in  large  masses  by  the  deficient 
conductivity  of  hot  metals.  It  thus  requires  much  experience 
to  judge  of  the  internal  temperature  from  the  appearance  of 
the  outside  of  the  mass. 

These  strains  increase  with  the  maximum  temperature  at- 
tained, being  greatest  in  the  ingot. 

They  also  increase  with  the  area  of  cross  section  of  the  mass, 
so  that  it  is  well  to  defer  the  hardening  until  the  pieces  are  as 
nearly  as  possible  of  their  finished  dimensions. 

Uneven  forging  produces  "hammer  strain"  which  is  re- 
Heved  by  annealing. 

Difference  in  section  causes  differences  in  rate  of  cooling, 
so  that  it  is  well  to  quench  the  thicker  portions  of  irregular 
masses  first. 

Other  things  being  equal,  internal  strain  increases  with  the 
grade  of  steel. 


*  This  is  probably  the  original  Damascus  steel,  which  has  been  imitated 
by  the  moderns  by  twisting  together  and  welding  wrought  iron  and  steel 
as  in  shot-guns. 


56  XV. METALLURGY. 


VII.  GUN   CONSTRUCTION. 

I.    BUILT-UP  GUNS. 

The  operations  are  substantially  as  follows : 

Casting  Ingot. 

For  forgings  such  as  tubes  and  jackets  the  ingot  is  often 
cast  square,  as  shown  in  Figure  25.  For  short  pieces  like 
hoops,  it  is  sometimes  cylindrical.  In  order  to  obtain  solid 
metal  and  to  free  it  from  slag,  sand  and  other  impurities  a 
given  amount  of  the  top  and  bottom  of  each  ingot  is  cut  off 
and  discarded  during  the  process  of  forging. 

The  ingot  is  sometimes  cast  hollow.  But  this  is  objection- 
able, for  it  transfers  the  unsoundness  found  in  the  centre  of  a 
solid  casting  to  the  middle  of  the  walls  of  the  gun. 

Coring. 

The  ingot  may  then  be  trepanned  by  a  sort  of  cylindrical 
saw  by  which  a  solid  core  is  removed.  This  rapidly  removes 
the  more  porous  portions  of  the  ingot,  which  are  in  a  more 
valuable  form  for  minor  purposes  than  the  shavings  from 
ordinary  boring.  This  operation  sometimes  precedes  and 
sometimes  follows  the  forging,  depending  upon  what  tools  the 
plant  affords  and  also  upon  the  size  of  the  gun. 

Forging. 

For  solid  ingots  the  work  is  constantly  rotated  during 
forging  by  means  of  the  porter-bar,  which  is  a  long  handle 
clamped  to  the  tong-hold.  A  sling  chain  around  the  drum 
forms  a  fulcrum.  Man  or  steam  power  is  used  according  to 
the  size  of  the  work. 

Cored  tubes  and  jackets  are  forged  on  a  fixed  mandrel  to 
approximately  their  finished  dimensions. 

Blanks  for  hoops  are  cut  off  the  ingot  and  upset,  or  hammered 
lengthwise  into  a  cheese-like  form.  After  punching  they  are 
treated  as  described  page  44,  or,  instead  of  rolling,  they  are 


XV. — METALLURGY.  57 


forged  on  a  mandrel.     The  choice  of  operations  depends  on 
the  length  of  the  hoop  and  the  facilities  available. 

After  every  operation  the  piece  is  carefully  chipped  by  hand 
to  remove/////?,  seams  and  cold  shuts. 

Treatment  and  Tests. 

The  term  treatment  applies  to  the  methods  employed  to 
affect  the  structure  of  steel,  viz.,  annealings  hardening  and 
re-annealing.    The  sequence  of  the  tests  is  important. 

The  *' hammer  strain"  is  relieved  by  annealing.  Annealing 
also  facilitates  the  reduction  by  cutting  tools  to  the  rough- 
finished  sizes  required  for  oil-hardening. 

After  annealing,  tests  of  the  metal  are  made  to  discover  its 
characteristics,  and  thus,  to  a  certain  extent,  to  regulate  its 
subsequent  treatment. 

The  pieces  are  then  rough-bored  and  turned  to  nearly  their 
finished  size. 

They  are  afterwards  oil-hardened  (generally  called  "oil- 
tempered")  by  being  uniformly  heated  to  W  in  a  furnace 
constructed  with  reference  to  the  shape  of  the  heated  piece, 
e.g.  tubes  in  a  vertical  flue,  through  many  ports  in  the  sides 
of  which  flame  enters  tangentially  and  hoops  in  an  ordinary 
low  furnace.  Each  piece  is  then  immersed  with  its  axis 
vertical  in  a  large  tank  of  oil,  holding  many  tons. 

The  tank  is  surrounded  by  a  jacket  through  which  a  stream 
of  water  flows  with  required  velocity.  The  oil  is  also  caused 
to  circulate  by  suitable  arrangements. 

The  pieces  are  re  an?tealed  *  to  remove  the  internal  strain 
due  to  hardening.  For  this  they  are  slowly  heated  to  a  low, 
red  heat  and  allowed  to  cool  very  slowly.  This  heat  improves 
the  structure,  but  may  slightly  reduce  the  strength  of  the 
metal. 


*  This  is  properly  tempering. 


XV. — metallurgy; 


Tests  of  the  metal  are  again  made  to  see  if  it  fulfils  the 
necessary  requirements. 

Assembling. 

The  parts  are  then  turned  and  bored  to  finished  dimensions 
and  assembled  by  shrinkage,  the  interior  diameter  of  the  out- 
side cylinder  to  be  assembled  being  finish-bored  to  the  diam- 
eter prescribed  for  the  contact  surface,  and  the  exterior  diam- 
eter of  the  surface  upon  which  it  is  to  be  assembled  being 
turned  to  the  excess  prescribed  for  the  shrinkage.  The  eff"ect 
of  the  shrinkage,  which  follows  the  heating  of  the  outer 
cylinder  so  that  it  may  pass  over  the  inner  one,  is  sometimes 
to  bring  the  surfaces  in  contact  within  the  range  of  molecular 
cohesion.  This  phenomenon  may  sometimes  be  seen  even 
between  cold  bodies.  When  the  steel  plugs,  used  to  gauge 
the  calibre  of  small-arms,  being  chemically  clean,  enter  forci- 
bly a  clean  bore,  they  are  sometimes  lost  through  ''freezing." 

The  hoops  are  secured  by  being  screwed  together,  but 
preferably  by  interlocking  projections  that  slip  by  each  other 
when  expanded  by  heat,  figure  47. 

The  policy  of  our  government  with  regard  to  gun  con- 
struction has  been  to  obtain  from  private  manufacturers  the 
forgings  rough-bored  and  turned,  and  to  finish  and  assemble 
the  various  parts  in  its  own  shops. 

IL    STEEL   CAST    GUNS. 

Objections. 

The  economical  advantages  of  this  process,  which  consists 
in  making  the  gun  of  a  single  steel  casting  after  the  manner 
formerly  adopted  for  cast-iron  guns,  are  off'set  by  the  follow- 
ing objections: 

I.   Mechanical. 

1.  The  enormous  increase  of  the  masses  to  be  handled  due 
to  the  weight  of  the  sinking  head,  which,  unless  its  functions 
can  be  replaced  by  other  means,  may  weigh  almost  as  much 
as  the  ingot  itself. 


XV. — METALLURGY. 


A  Steel-cast  gun  weighs,  in  the  rough,  about  3  times  as 
much  as  the  heaviest  ingot  required  for  a  built-up  gun  of  the 
same  calibre. 

2.  The  difficulty  of  making  molds  strong  enough  to  retain 
the  high  columns  of  metal  required  by  modern  powder. 

3.  The  loss  in  cutting  up  the  sinking  head,  for  re-melting 
or  in  disposing  of  failures. 

II.  Constitutional. 

1.  The  vesiculation,  impossible  to  correct  by  forging. 

2.  The  effect  on  crystallization  due  to  slow  cooling,  also 
impossible  to  correct  by  forging. 

3.  The  segregation  of  elements  of  different  densities  in 
cooling. 

4.  The  internal  strains  developed  in  cooling  castings  which, 
for  the  heaviest  guns,  cast  hollow,  would  possibly  be  60  or 
80  feet  high,  with  walls  3  or  4  feet  thick.  If  cast  solid,  this 
thickness  would  be  increased. 

Remark.  This  class  of  objections  may  possibly  be  over- 
come with  increased  experience  in  the  treatment  of  the  fluid 
metal,  and  by  annealing  the  gun  after  casting. 

Such  experience  must  be  costly,  for  it  can  be  acquired 
only  by  dealing  with  masses  approximately  as  great  as  those 
of  the  guns  themselves. 

III.  Structural. 

1.  The  impossibility  of  making  physical  or  chemical  tests 
of  internal  specimens. 

2.  The  impossibility  of  adapting  the  composition  of  con- 
centric parts  to  their  specific  functions  by  the  principle  of 
*' Varying  Elasticity,"  to  be  hereafter  discussed. 

3.  The  neglect  of  the  principle  of  "Initial  Tension"  by 
which  the  inner  parts  may,  by  preliminary  compression,  be 
prepared  for  the  strain  of  extension  on  firing.  This  principle 
is  ilhistrated  when  a  blacksmith  shrinks  on  a  tire. 

IV.  Historical. 

1.  Krupp's  original  guns,  which  were  massive   forgings, 


CO  XV. — METALLURGY*. 


have  been  gradually  replaced   by  guns   of  increasing   com- 
plexity of  structure. 

2.  The  only  recorded  failures  in  built-up  guns  have  occurred 
in  the  large  masses  constituting  the  tube  ;  sometimes  when 
unsupported,  as  in  the  chase;  or  when  imperfectly  supported, 
as  when  a  steel  tube  was  surrounded  by  a  jacket  of  ductile 
wrought  iron.  This,  having  been  expanded  beyond  its  elastic 
limit,  failed  to  support  the  tube,  which,  on  further  firing, 
cracked. 


XVI. — PROJECTILES. 


CHAPTER  XVI. 

PROJECTILES. 

Definition. 

Functionally  speaking,  a  projectile  is  a  vehicle  for  the 
transfer  of  energy  to  a  disconnected  object. 

The  energy  transferred  may  be  wholly  kinetic,  as  when 
the  projectile  acts  by  impact  only.  It  may  be  wholly  potential, 
as  when  the  kinetic  energy  of  the  envelope  of  the  mass  may 
be  neglected  in  comparison  with  the  potential  energy  of  its 
contents.  And  it  may  be  of  both  kinds,  as  when  the  kinetic 
energy  of  the  envelope  is  considerable. 

SECTIONAL  DENSITY. 

On  account  of  the  work  done  on  the  intervening  resist- 
ances, the  energy  actually  transferred  to  the  object  will 
always  be  less  than  that  originally  imparted  to  the  projectile. 

The  resistance  to  penetration  offered  by  the  intervening 
medium  and  the  object,  other  things  being  equal,  varies 
directly  with  the  area  of  cross-section,  a^  at  right  angles 
to  the  trajectory.     Let  us  call,  d,  the  diameter  of  the  circle 

whose  area  is,  «,  and  F=f—- —  the  total  resistance  causing 

retardation. 

The  retardation,  which  for  a  given  projectile  is  propor- 
tional to  the  loss  of  energy  per  unit  of  path,  will,  for  differ- 
ent projectiles  meeting  the  same  resistance,  vary  inversely 
with  the  mass  of  each  projectile;  or,  calling; 


XVI. — PROJECTILES. 


p,  the  retardation  in  the  direction  of  the  axis  of  Xj 
M,  the  mass  of  the  projectile; 
E,  the  energy  in  the  direction  of  X; 
we  have,  neglecting  variations  in  g; — 

_dE    \    _gp7t    d"^    _      d^ 

^~"d^"M~  ~T~  'W^W*  (-^^ 

in  which  k,  is  some  function  of  the  pressure  per  unit  of  area, 

/,  which  pressure  will  vary  with  the  veloucity,  the  meridian 

section  and  the  nature  of  <^he  surface  of  the  projectile.* 

d^ 
The  ballistic  coefficient^  or  coefficient  of  retardation  ^2,^  -— 

is  called,  may  therefore  be  used  to  compare  the  inherent 

capacities  of  projectiles  for  retardation;  and  the  reciprocal 

W 
of  this  expression,  or  —-^  which  is  called  the  j-^<r//^^/dr/^<?;zj/(>', 

may  be  used  to  compare  their  inherent  capacities  to  over- 
come resistances.  In  English  measures  ^is  taken  in  pounds, 
and  d  in  inches. 

VARIATIONS    IN    SECTIONAL    DENSITY. 

Causes. 

The  sectional  density  of  a  projectile  may  be  increased  as 
follows: — 

I.  If  the  dimensions  are  constant,  by  increasing  the  mean 
density. 

II .  If  its  mean  density  is  constant,  by  varying  its  dimen- 
sions, viz. : — 


*  Since  the  form  and  dimensions  of  a  projectile  are  independent  of  its 
velocity,  and  since  the  effect  upon  p  of  variations  in  the  meridian  section 
and  the  nature  of  the  surface  is  small  compared  with  those  which  result 
from  changes  in  its  diameter  and  weight,  and  disappears  when  similar 
projectiles  are  compared;  we  may  for  the  present  consider,  k,  for  any  pro- 
jectile as  constant,  so  that  the  value  of  p  may  be  considered  to  vary  only 
With  the  relation  between  d^  and   W% 


XVI. — PROJECTILES. 


1.  If  its  proportions  are  constant,  by  increasing  its  calibre; 
since  w  varies  as  d^^  while  a  varies  only  as  d}. 

2.  If  the  calibre  is  constant,  by  increasing  the  weight. 

3.  If  the  weight  is  constant,  by  decreasing  the  calibre. 
All  these  changes  virtually  lengthen  the  projectile. 

Effects  on  Flight. 

Increasing  the  sectional  density  of  a  projectile  which  has 
a  given  initial  velocity  increases  its  range  and  penetration, 
since  the  loss  of  energy  over  a  given  path  is  diminished.  It 
may  also  increase  its  accuracy,  since  the  time  of  flight  over 
a  given  path,  and  therefore  the  effect  of  various  perturbat- 
ing  causes  may  be  diminished.  The  penetration  is  still 
further  increased  by  increasing  the  indeformability  of  the 
material  of  which  the  projectile  is  composed,  so  that  the 
work  of  deformation  on  impact  may  be  done  rather  by  the 
projectile,  than  upon  it. 

But,  owing  to  the  non-coincidence  of  the  centers  of  mass 
and  of  the  area  exposed  to  the  resistance  of  the  air, 
during  the  flight  of  an  oblong  projectile  a  couple  is  formed 
which  tends  to  cause  the  projectile  to  tumble  or  revolve 
about  a  transverse  axis.  This  diminishes  its  sectional  den- 
sity and  makes  it  variable.  Such  projectiles  are  therefore 
given  the  rifle  motion,  which  impresses  upon  them  sufficient 
angular  velocity  about  the  longer  axis  to  make  this  a  stable 
axis  of  rotation,  and  therefore  to  make  their  sectional  den- 
sity constant  and  a  maximum.  The  same  reason  applies  in 
a  less  degree  to  spherical  projectiles,  in  which  the  centres 
of  mass  and  of  figure  can  rarely  be  made  to  coincide. 

Effect  upon  the  Gun. 

Increasing  the  length  of  an  oblong  projectile  increases 
its  tendency  to  tumble,  and  hence  requires  a  greater  energy 
of  rotation.  This  diminishes  the  kinetic  energy  of  transla- 
tion due  to  the  conversion  of  a  given  charge.     In  a  certain 


XVI. — PROJECTILES. 


sea  coast  rifle  the  rotary  energy  amounts  to  about  0.01  of 
the  total  muzzle  energy. 

Also,  since  increasing  the  sectional  density  increases  the 
mass  to  be  moved  per  unit  of  sectional  area,  a  given  accel- 
eration requires  an  increase  in  the  intensity  of  the  gaseous 
pressure  per  unit  of  area.  Therefore,  since  V=/adt,  to 
obtain  a  given  initial  velocity  with  a  projectile  of  which  the 
sectional  density  has  been  increased,  the  stress  upon  the 
gun  must  also  be  increased  unless  special  provision  be  made 
by  the  methods  indicated  in  Chapter  XI. 

Owing  to  the  weakness  of  cannon  in  use  when  the  rifle 
principle  was  first  applied,  the  increase  in  sectional  density 
required  a  reduction  in  the  initial  velocity;  this,  although 
compensated  for  by  greater  accuracy  and  longer  ranges, 
caused  the  initial  portions  of  the  trajectory  to  be  more 
curved  than  with  the  spherical  projectiles  formerly  em- 
ployed. See  Chapter  I.  Consequently,  the  general  adoption 
of  oblong  projectiles  was  delayed  until  the  necessary  im- 
provements in  the  gun  and  its  ammunition  had  been  per- 
fected.    See  Chapter  XIII. 

Comparison  of  Forms. 

Although  the  oblong  form  is  universally  employed  in  new 
constructions,  the  following  comparison  illustrates  some  of 
the  reasons  influencing  and  opposing  the  change  of  form. 

Advantages  of  Oblong  Projectiles, 

The  form,  capacity  and  sectional  density  may  be  altered 
indefinitely,  with  the  advantages  noted  in  the  text.  The 
following  incidental  advantages  also  exist: 

Projectiles  of  the  same  caliber,  but  of  different  natures, 
or  mean  densities,  may  be  made  of  the  same  weight;  so  that 
they  may  be  fired  at  the  same  ranges  with  the  same  angles 
of  projection. 


XVI. — PROJECTILES. 


The  oblorg  form  facilitates  the  operation  of  fuzes  which 
act  by  impact;  since  the  poinf-.  and  direction  of  the  impact 
can  be  predicted. 

Disadvantages  of  Ohlofig  Projectiles. 

The  centers  of  mass  and  of  pressure  do  not  coincide; 
they  are  more  expensive;  the  liability  to  injury  of  the  soft 
metal  device  by  which  they  are  rotated  requires  greater 
care  in  their  transportation  and  may  interfere  in  their 
loading;  in  ricocheting  over  land  or  water  their  rebounds 
are  much  less  certain  and  regular,  both  in  altitude  and 
direction.  The  rotation  of  rifled  projectiles  of  the  explosive 
class  tends,  upon  bursting,  to  scatter  their  fragments  unduly 
beyond  the  plane  of  the  trajectory.  The  curvature  of  the 
trajectory  at  short  ranges  is  increased. 

MATERIAL. 

The  principle  of  sectional  density  mainly  determines  the 
selection  of  the  proper  material  for  a  projectile,  with  regard 
to  its  behavior  in  the  gun,  in  the  air,  and  upon  the  object. 

Its  application  is  so  apparent  that  only  a  few  of  the  minor 
properties  of  the  materials  employed  will  be  mentioned. 

Stone  was  employed  originally  in  catapults  and  continued 
to  be  used  in  cannon  by  the  Turks  as  late  as  1807. 

Lead  is  suitable  for  use  against  animate  objects  only,  since 
in  large  cannon  it  is  disfigured  and  even  partially  melted. 

Wrought  Iron  in  large  masses  is  expensive,  as  it  requires 
welding  and  forging;  it  is  also  too  soft. 

Cast  Iron  was  until  recently  exclusively  used  for  artillery 
projectiles  on  account  of  its  fusibility  and  its  small  original 
cost.  When  cast  in  molds,  so  that  the  point  cools  in  con- 
tact with  a  cast  iron  chill,  while  the  body  cools  more  slowly 
in  sand,  its  local  hardness,  crushing  strength  and  density 
are  greatly  increased,  without  causing  brittleness  in  that 


XVI. — PROJECTILES. 


portion  cooled  in  the  sand.  Against  the  wrought  iron  armor 
formerly  employed,  such  projectiles  are  indeformable;  but 
they  are  pulverized  against  the  steel-faced  and  chilled  iron 
armor  of  the  present  day.  For  ordinary  purposes  cast  iron 
is  still  generally  employed. 

Steel  possesses  all  the  qualities  required  in  a  projectile, 
but  is  costly.  It  is  used  in  two  forms,  both  of  which  are 
usually  oil-tempered. 

1.  Forged;  including  for  special  purposes,  rolled  or  drawn 
steel  tubes.  This  form  of  steel,  especially  when  alloyed 
with  chromium,  is  so  far  the  best,  but  the  most  costly.  A 
9  inch  Whitworth  forged  steel  shell,  costing  $100,  or  12 
times  as  much  as  a  similar  projectile  of  chilled  cast  iron,  has 
been  fired  three  times  through  wrought  iron  12  inches  thick. 

2.  Steel  cast  projectiles  have,  owing  to  their  greater  cheap- 
ness, been  much  experimented  with;  but,  for  the  reasons 
given  in  Chapter  XV,  have  so  far  proved  inferior  to  those 
that  are  forged. 

SPHERICAL  DENSITY. 

W 
Since  the  sectional  density,  -— ,  of  similar  projectiles  in- 
creases with  the  caliber,  if  we  divide  the  sectional  density 

W 
by  the  caliber  we  shall  obtain  a  constant,  -73-,  which  expresses 

the  weight  per  unit  of  volume  of  a  cube  whose  weight  is 
equal  to  that  of  the  projectile  and  whose  height  is  equal  to 
the  diameter  of  the  bore.  This  is  taken  as  the  measure  of 
the  spherical  density  of  the  projectile. 

Since  all  spherical  solid  shot  of  the  same  material  are  simi- 
lar, their  spherical  density  is  constant,  and  may  therefore  be 
taken  as  the  unit  by  which  to  measure  the  spherical  density 
of  oblong  projectiles  of  the  same  material. 

Expressing  the  spherical  density  by  S^  and  the  weight  in 


XVI. — PROJECTILES. 


pounds  of  a  unit  of  volume  of  the  material  by  S,  we  have 
for  a  spherical  solid  shot,  of  which  the  volume  is  F, 


(7)'- 


ci^         d'  ~3  \d J    ~      3        8* 

For  projectiles  made  of  iron,  6  may  be  taken  as  %  pound, 
and  7t  may  be  taken  approximately  as  3.0;  therefore 

^.,  _  _  _  c, 

and  for  an  oblong  iron  projectile  in  terms  of  S^^, 
^   _W'    1  _  8  W 

S^i,  therefore,  expresses  the  effective  increase  in  density 
that  arises  from  elongating  the  projectile. 

We  might  proceed  similarly  with  other  materials  having 
different  values  of  6;  but  it  is  convenient  to  retain  iSg}  as  a 
common  standard;  so  that,  in  general  terms,  S  may  be  taken 
to  measure  the  number  of  times  that  the  mass  of  the  inscribed 
solid  iron  sphere  is  contained  in  that  of  the  projectile  con- 
sidered. 

Unless  the  caliber  be  fixed,  the  spherical  and  sectional 
densities  of  projectiles  vary  independently  of  each  other. 

The  spherical  density  of  the  first  oblong  projectiles  used  in 
cannon  in  1859,  was  about  2.0;  but  recent  improvements  in 
guns,  powder  and  projectiles  have  increased  it  from  about  3.0 
m  1880,  to  about  4.5  in  1887,  the  muzzle  velocity  not  being 
correspondingly  reduced. 

If  all  projectiles  made  of  the  same  material  had  the  same 
mean  density  and  the  same  form,  their  spherical  densities 
would  be  a  function  of  their  lengths.  But  as  such  is  not  the 
case,  their  length  is  independently  stated,  generally  in  cali- 
bers. In  fact,  the  caliber  is  getting  to  be  taken  as  the  general 
unit  of  measure  of  all  the  linear  dimensions  relating  to  the 
interior  of  the  piece. 


dim'B.t^' 


XVL — l^ROjECTtLEg. 


Corollary, 

Referring  to  the  discussion  on  page  7,  we  see  that  the 
weight  in  pounds  of  a  sohd  spherical  cast  iron  projectile  is 
very  nearly  equal  to  the  cube  of  its  radius  in  inches.  This 
affords  an  easy  method  of  approximating  to  the  weight  of 
an  oblong  projectile  when  the  type  of  gun  from  which  it  is 
to  be  fired  is  known. 

RIFLING. 

History. 

The  invention  of  rifling  by  Gaspard  Zoller  of  Vienna  is 
said  to  have  been  made  soon  after  the  discovery  of  America. 
The  first  rifle  grooves  were  made  straight,  and  intended  only 
to  facilitate  the  loading  of  tightly  fitting  bullets.  The  advan- 
tages of  the  spiral  groove,  which  were  accidentally  dis- 
covered, were  not  applied  to  oblong  projectiles,  even  in  small 
arms,  until  about  100  years  ago,  at  which  time  the  subject 
was  thoroughly  discussed  by  the  eminent  mathematician 
Eobins.  It  is  worthy  of  remark  that  to  Robins  we  owe  the 
first  practical  apparatus  for  the  measurement  of  the  velocity 
of  projectiles;  a  pendulum  into  which  the  projectile  was  fired, 
and  from  the  nwDmentum  of  which  that  of  the  projectile 
could  be  computed. 

The  general  adoption  of  the  rifle  principle  for  small  arms 
was  retarded  by  the  difliculty  found  in  loading  the  rifle:  this 
w^as  generally  accomiplished  by  the  blows  of  a  mallet  on  a  stout 
iron  ramrod.  For  cannon,  attempts  were  made  at  an  early 
date  and  are  frequently  renewed,  to  impart  the  rifle  motion 
by  the  action  of  the  gas,  or  of  the  air  upon  spiral  grooves 
or  wings  formed  upon  the  projectile.  Except  for  low  veloci- 
ties, all  such  experiments  have  failed  to  act  with  certainty, 
and  the  end  has  been  attained  only  by  the  positive  means 
mentioned  in  Chapter  I. 


XVI. — PROJECTILES. 


Twist. 

The  inclination  of  a  rifle  groove  at  any  point  is  determined 
by  the  angle  which  its  tangent  at  that  point  makes  with  the 
axis  of  the  bore.     Twist,  is  the  term  generally  employed  to 
express  this  inclination. 
Classification  of  Twists. 

When  the  inclination  of  the  groove  to  the  axis  of  the  bore 
is  constant,  the  twist  is  called  Mniform.  When  it  increases 
from  the  breech  to  the  muzzle,  the  twist  is  increasing. 

Figure  1  shows  the  development  of  the  surface  of  a  bore 
rifled  with  uniform  and  increasing  twists.  Such  curves  are 
traced  for  the  construction  of  templets,  by  which  a  combined 
motion  of  rotation  and  translation  is  given  to  the  cutting  tool 
of  the  rifling  machine. 
Discussion. 

Let  q)  be  the  inclination  of  the  groove  at  any  point;  and 
oa  the  angular  velocity  imparted  to  the  projectile  from  being 
constrained  to  follow  in  the  groove  while  moving  in  the 
direction  of  the  axis  with  a  velocity  of  translation  v.  Let  r 
be  the  radius  of  the  projectile. 

We  may  consider  the  velocity  along  the  groove  to  be  the 
resultant  of  two  component  velocities  at  right  angles  to  each 
other;  viz.:  z;  and  f/ tan  q).  The  latter  imparts  to  a  point 
on  the  surface  of  the  projectile  a  tangential  velocity 
r  Go=^v  tan  cp.     Hence, 

V 

CD  =z  tan  cp     •  (2) 

That  is  to  say  that  when  the  twist  is  uniform,  the  angular 
velocity  increases  only  with  the  velocity  of  translation 
throughout  the  bore.  When  the  twist  is  increasing,  the 
angular  velocity  further  increases  from  this  cause;  and  other 
things  being  equal,  it  increases  as  the  caliber  diminishes. 

Since  the  muzzle  velocity  of  a  given  projectile  is  fixed  by 
independent   considerations,  the   angular  velocity  at  the 


10  XVT. — PROJECTILES. 

muzzle  is  measured  by  the  tangent  of  the  angle  made  at  that 

point  by  the  tangent  to  the  groove  and  the  axis. 

If  /  be  the  time  required  to  make  one  revolution,  and  n 

be  the  length  in  calibers  over  which  the  projectile  must  pass 

in  order  to  make  one  revolution,  we  have  from  Eq.  (2), 

ODrt       ^7tr        7t 
tan  ^  =  -— -  =  --—  =  -.  (3) 

The  twist  is  accordingly  generally  expressed  in  terms  of  n. 

It  has  been  found  that  for  ordinary  artillery  projectiles, 
about  three  calibers  long,  the  requisite  steadiness  is  given 
by  imparting  to  the  surface  of  the  .projectile  a  tangential 
velocity  of  about  200  f.  s.  at  the  muzzle  of  the  gun.  Hence, 

7t  V 

200  =  r  ci?  =  tan  a>.  F=  -  V  .\  n—n  — —  .         (4) 
n  200  ^  ' 

The  value  of  n  at  the  muzzle  of  the  piece  has  generally 
been  determined  empirically  as  above  indicated;  a  safe 
margin  being  allowed,  smce  no  objection  to  a  moderate  in- 
crease in  twist  exists  but  that  pertaining  to  a  diminished 
energy  of  translation,  and  to  the  increased  stress  upon  the 
piece. 

Recent  analysis  has  determined  the  minimum  twist  at  the 
muzzle  for  projectiles  of  varying  proportions. 

It  appears  from  this  analysis  that  n  is  constant  for  similarly 
proportioned  projectiles  of  the  same  material,  whatever  be 
the  caliber;  that  it  increases  as  the  radius  of  gyration  about 
the  axis  of  revolution  and  the  density  of  the  projectile  in- 
crease, and  as  the  radius  of  gyration  about  an  equatorial 
axis  diminishes.  Also,  that  the  above  value  for  the  surface 
velocity  is  only  approximate,  since  for  the  same  projectile 
this  may  safely  diminish  as  the  initial  velocity  diminishes. 
Tangential  Pressure  on  the  Rotating  Device. 

Since,  for  the  same  muzzle  velocity  of  translation,  the  sta- 
bility of  a  given  projectile  depends  only  on  the  angular 
velocity  which  it  has  acquired  at  the  muzzle;  it  appears  that 


XVI. — PROJECTILES.  11 


SO  far  as  this  is  concerned,  it  matters  not  whether  the  angular 
velocity  be  acquired  only  through  or,  the  acceleration  of 
translation,  or  through  the  combination  of  this  cause  with 
the  gradually  increasing  twist. 

In  the  first  case,  the  angular  acceleration,  will  be  greatest 
at  first,  when  the  gun  and  the  rotating  device  are  under 
their  maximum  strain,  and  will  diminish  as  they  become 
relatively  stronger;  thus  making  a  disadvantageous  distri- 
bution of  the  work  of  rotation,  although  the  quantity  of  work 

W 
done  will  be  constant  and  equal  to  -^ —  /^/  w^ 

2g 

k,  is  taken  as  about  0.8  r  in  the  linear  units  used  for  V, 

In  order  to  make  this  stress,  particularly  that  upon  the 
rotating  device,  constant  throughout  the  bore,  so  as  to  avoid 
either  excess  or  deficiency  in  strength,  the  angular  acceler- 
ation must  be  made  constant.  Herein  lies  the  value  of  the 
increasing  twist;  since  at  the  breech  the  diminished  value 
of  q)  will  compensate  for  the  increased  value  of  a\  and  con- 
versely toward  the  muzzle. 

The  determination  of  the  precise  form  of  the  developed 
groove  is  difficult,  both  theoretically  and  practically,  since 
the  constancy  of  a  depends  upon  the  properties  of  the 
powder  employed. 

It  was  thought  for  some  time  that  a  groove,  the  twist  of 
which  uniformly  increased  with  the  length  of  the  bore,  and 
having  as  its  development  a  parabola,  would  give  the  best 
results. 

Recent  practice  indicates  the  advantage  of  employing  a 

semi-cubic  parabola,  of  the  form  x^—2py,  which,  in  the 
case  illustrated  in  figure  2,  passes  from  a  value  of  n=50  at 
the  breech,  to  n=2D  at  the  muzzle.  Figure  2  shows  how 
variously  may  be  distributed  the  tangential  pressures.  To 
steady  the  projectile  on  leaving  the  bore,  it  has  been  thought 


12  XVI. — PROJECTILES. 


advisable  to  give  to  a  short  portion  of  the  rifling  neai  the 
muzzle  a  uniform  twist. 

MEANS  OF  ROTATION. 

I.    MUZZLE-LOADERS. 

Classification. 

The  first  rifled  pieces  were  muzzle-loaders,  and  hence  the 
projectile  was  necessarily  of  smaller  diameter  than  the  bore. 
Rotation  was  imparted  to  it  in  two  general  ways: 

1.  By  making  the  rotating  device  fit  the  grooves  before 
firing,  by  providing  the  projectile  with  suitable  ribs  or 
flanges. 

2.  By  making  the  device  fit  the  grooves  after  firing  by 
causing  it  to  be  expanded  by  the  powder  gases,  after  the 
manner  of  the  gas  check.     Chapter  VII. 

Operation. 

For  this  special  purpose,  and  in  all  cases  to  avoid  abrad- 
ing the  grooves,  the  rotating  device  was  made  of  a  softer 
metal  than  the  rest  of  the  projectile;  or,  if  formed  on  the 
body  of  the  projectile,  had  given  to  it  a  large  area  of  con- 
tact so  as  to  accomplish  the  same  result. 

Since  the  axis  of  such  projectiles  did  not  normally  coin- 
cide with  that  of  the  bore,  they  could  be  centered^  or  made 
concentric  with  the  bore,  only  by  chamfering  the  edge  of 
the  groove  giving  rotation,  or  by  some  similar  device,  the 
operation  of  which  was  uncertain. 
Comparison. 

Examples  of  the  first  class  are  shown  in  figures  3  and  4. 
Those  with  studs  were  until  recently  generally  employed  in 
Europe.  The  Whitworth  projectile,  the  surface  of  which  is 
a  twisted  prism,  is  a  type  of  this  class.  It  was  once  distin- 
guished, but  is  no  longer  employed  in  new  constructions. 

The  principal  advantage  of  this  class  is  that  the  projectiles 
are  certain  to  take  up  the  rifle  motion. 


XVI.— PR0JECTIL1E5.  13 


They  require  special  adjustment  to  the  gun,  both 
in  manufacture  and  in  loading;  the  escape  through  the 
windage  erodes  the  bore;  the  stud  holes  weaken  the  projec- 
tile, and  their  arrangement  in  tiers,  or  the  use  of  flanges 
renders  it  difficult  to  adapt  these  projectiles  to  the  increas- 
ing twist. 

Examples  of  the  second  class  are  seen  in  figures  5,  6,  7. 

Their  advantages  are  their  adaptation  to  any  gun  of  the 
proper  caliber  and  the  facility  with  which  they  can  be  load- 
ed, particularly  in  action.  The  former  advantage  led  to 
their  general  employment  during  the  Civil  War,  owing  to 
the  elasticity  of  the  conditions  then  prevailing.  Only  the 
weight  and  the  caliber  of  the  projectile  were  fixed ;  so  that 
inventors  were  free  to  adopt  many  ingenious  variations  of  the 
expanding  principle.  This  is  accordingly  known  as  the 
American  system.  It  answered  well  the  demands  of  the 
situation  but  was  uncertain  in  its  operation;  the  expansion 
sometimes  failing  and  the  entrance  of  the  powder  gases  be- 
tween the  body  of  the  projectile  and  the  rotating  device 
serving  sometimes  to  tear  this  from  its  seat.     See  figure  7. 

The  expanding  cup  has  sometimes  been  applied  to  pro- 
jectiles of  the  first  class  so  as  to  prevent  the  escape  of  gas 
above  cited. 

Examples  of  Class  II. 

The  Butler  and  Eureka  systems  are  the  principal  exam- 
ples of  the  second  class  retained  for  the  muzzle-loading 
cannon  still  in  service. 

The  Butler  System.  Figure  5. 
The  distinctive  feature  is  the  double  lip  formed  in  the 
expanding  ring.  The  outside  lip  is  expanded  into  the 
grooves,  while  the  inner  one  is  pressed  against  the  tenon 
on  the  base  of  the  projectile  with  an  intensity  proportional 
to  that  of  the  gaseous  pressure. 


14  XVI.— PROJECTILES. 


The  Eureka  Projectile.     Figure  6. 

The  base  of  the  projectile  is  a  frustum  of  a  cone  in  which 
the  grooves,  «,  are  cast.  The  expanding  brass  cup  fits  on 
the  frustum  and  is  prevented  from  turning  by  correspond- 
ing projections  on  its  inner  surface,  and  from  falling  off 
during  transportation  by  the  screw  plug,  b. 

On  firing,  the  cup  is  forced  forward  and  expanded  into 
the  grooves. 

II.    BREECH-LOADERS. 

In  breech-loading  cannon  the  chamber  is  of  larger  diam- 
eter than  the  bore,  and  permits  the  use  of  a  projectile  pro- 
vided with  a  compressible  device. 

Beside  the  advantages  named  in  Chapter  XI,  the  advan- 
tages of  this  class  are  certainty  of  action,  better  centering 
and  the  absence  of  windage.  These  qualities  have  caused 
their  general-  adoption  to  follow  that  of  the  cannon  in 
which  they  are  employed. 
History. 

Following  the  analogy  of  projectiles  for  small  arms,  it  was 
at  first  attempted  to  coat  them  with  lead,  cast  over  the  body 
of  the  projectile.  But  this  was  weak,  the  lead  fouled  the 
bore,  was  easily  deformed,  and  added  useless  weight  to  the 
projectile  when  it  was  fired  against  armor.  The  length  of 
the  bearing  prevented  the  use  of  the  increasing  twist,  and 
the  manner  of  applying  the  lead  tended  to  alter  the  struc- 
ture of  projectiles  of  hardened  steel.  Such  were  the  pro- 
jectiles used  by  the  Germans  in  the  war  of  1870. 

To  overcome  these  objections,  narrow  rings  or  bands  of 
copper,  which  is  much  stronger  than  lead,  were  placed  in 
pairs  at  equal  distances  from  the  centre  of  gravity.  Their 
diameter  was  equal  to  the  caliber  measured  between  the 
bottom  of  the  grooves,  or  slightly  greater,  while  that  of  the 
body  was  a  little  less  than  that  between  the  lafids.  Such 
projectiles  required  the  uniform  twist. 


XVI. — PROJECTILES.  16 


To  this  class  belongs  a  projectile  used  in  the  small 
Hotchkiss  cannon;  figure  9.  It  has  a  thin  sheet  brass  belt 
about  one  caliber  wide,  compressed  radially  into  a  shallow 
groove  of  equal  width  which  is  symmetrical  with  the  center 
of  gravity.  The  surface  of  the  groove  is  circumferentially 
fluted,  as  seen  in  figure  9.  When  the  piece  is  fired  the 
powder  gases  press  the  band  into  the  flutings,  forming  a 
series  of  rings,  figure  10,  which  permit  the  metal  to  flow 
backward  as  the  band  takes  the  rifling.  These  bands  are 
much  cheaper  to  make  and  weaken  the  projectile  less  than 
the  solid  rings  formerly  employed  in  these  projectiles. 
This  ingenious  method  is  confined  to  small  calibers. 
Present  Practice. 

The  increasing  twist  now  used  in  all  large  cannon  re- 
quires a  narrow  bearing,  which,  to  diminish  the  effect  of  the 
oblique  action  of  the  powder  gases  is  situated  in  rear,  at 
such  a  distance  from  the  base  of  the  projectile  as  to  give 
sufficient  shearing  strength  to  that  portion  lying  in  rear  of 
the  band. 

To  center  the  projectile  a  second  band  was  formerly 
placed  in  front,  but  this  has  been  replaced  by  a  very  slight 
enlargement  of  the  body  of  the  projectile  near  the  base  of 
the  head.     Figure  21. 
Position  of  the  Eotating  Band. 

Although,  for  ease  in  loading,  the  difference  of  diameter 
between  the  front  bearing  and  the  lands  is  made  as  small  as 
is  safe;  unless  certain  precautions  are  taken,  the  oblique 
action  of  the  powder  gases  —  in  a  manner  not  thoroughly 
understood  —  may  set  up  a  nutatory  or  oscillating  motion 
as  the  projectile  travels  through  the  bore.  This  leads  to 
inaccuracy,  reduces  penetration,  and  may  even  leave  the 
marks  of  the  rifling  on  the  front  portion  of  the  projectile. 

To  diminish  this  effect,  the  front  and  rear  bearings  should 
be  made  the  loci  of  conjugate  axes  of  suspension  and  oscil- 


16  XVI. — PROJECTILES. 


lation.  When  the  position  of  the  front  bearing  is  determined 
by  the  shape  of  the  projectile,  this  can  be  accompHshed  by 
swinging  the  projectile  as  a  pendulum  on  a  diameter  of  the 
front  bearing,  and  ascertaining  the  time,  /,  of  one  vibration. 
Then  the  band  should  be  placed  at  a  distance  from  it, 

I  =  g  l—\       since  f=7t\/  —   {Michie^  Eq.  404.) 

In  order  to  diminish  the  effects  of  the  oscillation  in  pro- 
jectiles in  which,  from  unavoidable  differences  in  manufac- 
ture, the  method  above  described  does  not  suffice,  the  width 
of  the  rotating  band  should  be  made  as  great  as  the  nature 
of  the  twist  permits.  It  is  usually  taken  as  about  one-tenth 
of  the  caliber. 


LONGITUDINAL  SECTION  OF  THE  PROJECTILE 

Profile. 

The  value  of  k  in  Eq.  (1)  depends  largely  upon  the  profile 
of  the  meridian  section  of  the  projectile  and  the  nature  of 
the  surface.  In  the  last  respect  breech-loading  projectiles 
of  the  last  class  have  a  decided  advantage  over  those  of  the 
first  class  of  muzzle  loading  projectiles,  since  the  atmocpheric 
friction  is  much  less.  This  has  required  revision  of  the 
ballistic  tables  computed  for  the  non-centered  studded  pro- 
jectiles for  which  these  computations  were  originally  made. 

The  resistance  of  the  air  is  not  affected  by  the  form  of 
the  extreme  point,  which,  even  if  flat,  is  supposed  to  carry 
along  with  it  a  pointed  core  of  compressed  air;  but  the  cur- 
vature of  the  head  of  the  projectile  is  of  great  importance 
in  that  it  affects  the  passage  of  the  stream  lines  of  air  past 
the  shoulder^  as  is  called  the  circle  of  tangency  between  the 
head  and  the  cylindrical  portion  of  the  projectile.  The  cur- 
vature of  the  head  is  expressed  by  the  length  of  the  radius 
of  curvature  in  calibers.  This  varies  from  1.5  to  2.0  calibers. 


XVI. PROJECTILES.  17 


The  form  of  the  base  is  also  of  importance,  in  that,  if  also 
curved,  it  facilitates  the  flowing  of  the  compressed  air  into 
the  vacuum  formed  in  rear  of  the  projectile  and  so  diminishes 
the  difference  of  pressure  upon  the  two  extremities  of  the 
projectile ;  to  which  difference  the  retardation  is  principally- 
due.  Examples  of  this  may  be  seen  in  the  Whit  worth  pro- 
jectile and  in  the  Hotchkiss  projectile,  already  described. 
This  advantage  is  not  generally  utilized,  as  it  tends  to  diminish 
the  sectional  density,  the  strength  of  the  base,  and  the  facility 
of  manufacture  and  of  stowage. 
Mass. 

The  mass  of  the  projectile  should  be  distributed  so  as  to 
bring  the  center  of  air  pressure  as  close  as  possible  to  the 
center  of  mass  so  as  to  diminish  the  overturning  moment  of 
the  resistance  of  the  air.  This  is  a  difficult  matter,  as  the 
direction  of  the  pressure  is  constantly  changing;  it  is  there- 
fore adjusted  empirically  by  firing  projectiles  so  weighted 
that  the  position  of  the  center  of  mass  may  be  varied 

INFLUENCE  OF  THE  CALIBER. 

Following  the  principle  of  similitude  by  which  cannon  of 
the  same  class  vary  their  linear  dimensions  in  a  given  ratio 
to  their  calibers,  it  appears: — 

1.  That  the  muzzle  energy  varies  with  the  charge  of 
powder,  or  as  the  cube  of  the  caliber. 

2.  That  the  capacity  to  convey  this  energy  to  a  distance 
varies  as  the  first  power  of  the  caliber. 

3.  That  the  terminal  energy  varies  as  a  power  of  the  caliber 
which  increases  from  about  3  at  the  muzzle  to  about  4  at  the 
extreme  range  of  the  smaller  of  two  pieces  considered. 

STRUCTURE    AND    MODE  OF  OPERATION. 

Projectiles  are  classed  according  to  their  structure  and 
mode  of  operation  as  follows : — 


18 


XVI. — PROJECTILES. 


1.  Solid  shot,  or  shot, 

2.  Shells. 

3.  Case  shot. 

T.   SHOT. 

Shot  are  used  for  penetration,  generally  of  armor  and  in 
small  arms  against  animate  objects.  For  cannon  they  are 
confined  almost  wholly  to  the  sea  coast  service.  In  order 
to  diminish  the  effects  of  internal  strain  due  to  differences 
in  the  rate  of  cooling,  shot  are  made  not  wholly  solid  but 
with  an  empty  concentric  cavity  or  core,  figure  11.  In  such 
projectiles  the  point  is  carefully  preserved. 

II.    SHELLS. 

The  increase  in  sectional  density  resultmg  from  making 
spherical  projectiles  solid,  having  been  attained  by  a  change 
of  form,  solid  shot  are  now  replaced  by  those  which  are 
hollow  and  whioh  can  therefore  convey  energy  in  a  form 
unaffected  by  retardation. 

Shells  are  hollow  projectiles  containing  an  explosive  and 
generally  a  fuze  for  its  ignition  at  any  desired  point  of  the 
trajectory,  The  fuze  may  operate  at  a  distance  which  is  a 
function  of  the  time  of  flight,  when  it  is  called  a  time  fuze; 
or  the  explosion  may  result  more  directly  from  the  arrival 
of  the  projectile  at  the  point  of  impact.  Such  are  called 
impact  fuzes.  Each  class  of  fuzes,  as  will  be  seen,  has  its 
special  province. 

The  size  of  the  cavity  depends  upon  the  specific  function 
of  the  projectile.  If  this  is  intended  to  convey  energy  mainly 
in  the  kinetdc  form,  the  smaller  the  cavity,  the  greater  is  the 
sectional  density,  and  the  more  violent  is  the  explosive 
required.  If  the  energy  is  to  be  mainly  potential,  the  larger 
the  cavity  the  better  the  effect,  provided  that  the  resistance 
of  the  projectile  to  the  shock  of  discharge  is  not  unduly 
diminished. 


XVI. — PROJECTILES.  19 


The  number  ot  pieces  resulting  from  an  explosion,  and 
the  facility  with  which  the  bursting  charge  wili"  operate,  in- 
crease with  the  brittleness  of  the  material  and  with  the 
completeness  with  which  conversion  occurs  before  rupture 
of  the  envelope  occurs.  Since  for  firing  against  troops  frag- 
ments below  about  one  ounce  in  weight  are  not  considered 
dangerous,  it  is  desirable  to  increase  the  number  of  fragments 
of  about  this  weight  as  much  as  possible  and  so  to  compensate 
for  the  large,  single  mass  formed  by  the  base  of  the  shell. 

The  sectional  density  of  the  fragments  approaches  con- 
stancy and  practically  increases  as  they  approach  the  spher- 
ical or  cubical  form ;  therefore,  many  devices  have  been 
employed  to  regulate  the  rupture  of  such  projectiles,  as  by 
making  the  walls  double,  figure  12 ;  by  giving  to  the  cavity 
a  polyhedral  form ;  or  by  grooving  it  spirally  so  as  to  dimin- 
ish the  tendency  to  burst  in  a  meridian  plane. 

This  appears  from  the  following  elementary  analysis. 

Tet  R  and  r,  be  the  exterior  and  interior  radii  of  a  shell, 
the  tenacity  of  which  is  T,  supposed  uniform  throughout  the 
section.  Then,  for  the  meridian  rupture  of  a  unit  of  length 
the  necessary  pressure  will  result  from  the  equation — 

2r/  =  2(i?-r)r.-./=r('^-lY 

for  an  equatorial  or  transverse  rupture  we  have 

Operation. 

The  rupture  of  a  shell  will  occur  in  one  of  the  two  ways 
above  indicated  only  when  the  material  is  thin  and  inelastic,  as 
in  some  shrapnel  to  be  described.  When,  as  is  usually  the 
case,  the  projectile  has  thick  walls  (Chap.  V),  the  inner  con- 
centric layers  are  more  extended  than  those  outside,they  are  fis- 
sured until  fracture  is  determined  by  the  line  of  least  resistance, 


20  XVI.'— PROJECTILES. 


and  the  fragments  are  scattered  by  the  energy  remaining  in 
the  gases.  The  resistance  of  the  envelope  should  therefore 
be  kept  within  certain  Hmits. 

Shells  used  against  armor  are  pointed,  and  are  filled  and 
fuzed  from  the  rear.  They  replace  shot  whenever  possible 
since  their  penetration  can  be  made  almost  as  great,  and 
their  effects  after  penetrating  the  sides  of  a  vessel  are  much 
more  destructive  both  to  men  and  machinery. 

Against  masonry,  shell  serve  a  double  purpose;  first  to 
penetrate  the  wall  and  fissure  it  by  their  explosion;  and 
second,  by  throwing  out  the  fragments  to  present  a  fresh 
surface  for  the  next  blow. 

Shells  used  against  earthworks  should  contain  the  largest 
possible  bursting  charges.  Such  are  called  torpedo  shells. 
They  are  sometimes  made  6,  and  even  8  calibers  long  and, 
owing  to  the  vertical  angle  at  which  they  strike,  are  fired  with 
low  velocities  from  mortars  and  howitzers. 

A  grenade  is  a  form  of  shell,  generally  spherical,  intended 
to  be  thrown  by  hand  or  to  be  rolled  down  a  parapet  against 
masses  of  troops  making  an  assault. 

BURSTING    CHARGES. 

Gnnpowder. 

When  powder  is  used  it  is  preferably  of  fine  grain  and  of 
high  gravimetric  density.  Such  powder  in  firing,  has  a 
tendency  to  cake^  or  become  compressed  into  a  mass  of  such 
density  that  the  removal  can  be  accomplished  only  by  the 
chisel.  This  increases  with  the  length  of  the  charge  and 
evidently  tends  to  defeat  its  object. 

The  caking,  as  indicated  by  the  letters  a,  b,  c,  in  figure  13, 
results  from  three  causes;  viz.:  a,  from  the  shock  of  dis- 
charge; b,  from  the  rotation  of  the  projectile,  and  <r,  from 
the  shock  of  impact. 


XVI.— PROJECTILES.  21 


The  effect  is  to  compress  the  powder  and  diminish  its 
inflammability.  If  the  impact  be  sufficiently  resisted,  the 
solidified  mass  may  be  thrown  forward  with  such  energy  as 
to  cause  its  ignition.  To  diminish  caking,  the  cavity  is 
often  varnished;  and  to  delay  the  explosion  of  armor  piercing 
shell,  the  bursting  charge  is  sometimes  enveloped  in  flannel. 
On  the  other  hand,  where  promptness  is  required,  the  French 
place  loosely  in  the  cavity  a  small  wooden  prism,  figure  14, 
containing  on  two  of  its  sides  a  network  of  oblique  grooves 
through  which  the  gases  resulting  from  ignition  may  pene- 
trate the  indurated  mass.  A  slip  of  wood  is  tied  over  each 
grooved  surface  to  prevent  the  channels  from  becoming 
choked. 

The  bursting  charge  has  been  advantageously  made  of 
discs  of  concrete  powder,  strong  enough  to  resist  the  causes 
leading  to  a  and  b,  figure  13,  but  disintegrating  under  the 
influence  of  ignition.  Such  charges  require  to  be  filled 
through  a  hole,  the  size  of  which  is  objectionable. 
High  Explosives. 

Gun-cotton  is  not  injured  by  caking  and,  when  specially 
prepared,  does  not  readily  explode  on  impact.  This,  or  some 
equivalent  high  explosive,  appears  to  be  required  for  shells 
in  which  the  excessive  fragmentation  of  the  envelope  is  not 
objectionable.  This  objection  may  be  removed  by  using 
a  small  charge  of  dry  gun-cotton  in  a  shell  filled  with  water. 

A  high  explosive  is  particularly  required  in  armor  piercing 
shells;  these,  if  strong  enough  to  penetrate  the  armor,  may 
fail  to  burst  with  the  utmost  powder  charge  whrch  they  will 
contain  or  they  may  explode  harmlessly  before  penetration 
is  complete. 

The  comparative  insensibility  of  explosives  of  the  Bellite 
class  would  seem  to  fit  them  particularly  to  this  purpose; 
although  the  gx&dX  force  of  gun-cotton  makes  it  well  adapted 
for  use  against  earthworks.     Its  explosion  is  said  to  reduce 


22  XVI. — PROJECTILES. 


a  large  spherical  zone  of  earth  to  a  pulverulent  form,  by 
which  its  removal,  and  the  exposure  of  the  masonry  which 
it  is  intended  to  protect,  are  facilitated. 

Sizft  of  Cavity. 

Great  advantage  has  been  found  to  result  from  increasing 
the  size  of  the  cavity  by  making  the  envelope  of  the  shell 
of  thin  steel  tubing.  A  12  pound  shell  so  made  was  found 
more  effective  against  earthworks  than  a  50  pound  shell  of 
cast  iron.  To  produce  their  full  effect,  such  projectiles 
require  an  independent  steel  base,  concave  on  its  interior 
surface,  so  that  it  may  be  expanded  against  the  walls  instead 
of  being  driven  outward  by  the  explosion  before  the  powder 
is  entirely  converted  into  gas. 


INCENDIARY    PROJECTILES, 

Although  the  explosion  of  the  bursting  charge  may  suffice 
to  ignite  the  splintered  fragments  of  wooden  structures, 
greater  certainty  in  the  effect  results  from  filling  the  shell 
with  an  incendiary  composition  ignited  by  the  discharge 
and  flaming  through  specially  constructed  apertures  in  its 
walls.  Such  projectiles,  called  carcasses,  and  also  red-hot 
shot,  were  formerly  employed  against  wooden  vessels. 

To  this  class  may  be  referred  light  balls,  thrown  at  short 
ranges  to  burn  on  the  ground  and  illuminate  the  works  of 
an  enemy  during  a  siege.  To  prevent  their  extincti*on,  they 
were  made  to  contain  a  loaded  shell  or  a  number  of  loaded 
pistol  barrels. 

A  more  recent  form  consists  of  a  shell  containing  a  para- 
chute which  is  distended  when  the  shell  explodes,  and, 
when  carried  over  the  enemy's  works  by  the  wind,  illumi- 
nates them  by  the  light  of  a  mass  of  incendiary  composition 
suspended  beneath  it. 

For  modern  warfare  such  devices  are  superseded  by  the 


XVI. PROJECTILES.  23 


electric  light,  projected  from  under  cover  by  a  reflecting 
surface. 

III.    CASE    SHOT. 

Where  concentration  of  energy  upon  a  given  point,  and, 
therefore,  accuracy  is  required,  shell,  or  preferably  solid 
shot  are  used;  but  where,  owing  to  the  dispersion  of  the  ob- 
jects and  their  inferior  resistance  the  energy  should  be 
distributed,  as  in  fowling  pieces,  case  shot  are  employed. 

Case  shot  consist  of  a  number  of  small  projectiles,  which 
we  may  call  the  cluster,  contained  in  an  envelope;  according 
to  the  method  of  their  liberation  from  which  they  are  divided 
into  two  classes. 

1.  Canister  and  grape  shot,  which  separate  at  the  muzzle 
of  the  piece  in  consequence  of  the  shock  of  discharge.  The 
general  name,  case,  is  now  usually  reserved  for  this  variety. 

2.  Shrapnel,  which  separate  at  a  distance  in  consequence 
of  the  explosion  of  a  small  bursting  charge,  contained  with- 
in the  envelope. 

These  projectiles  forcibly  illustrate  the  principle  of  sec- 
tional density  in  regard  to  the  behavior  of  the  projectile  as 
a  whole,  and  to  the  operation  of  the  component  parts,  includ- 
ing the  fragments  of  the  envelope. 
Operation. 

The  fragments  separate  in  what  is  called  the  sheaf,  or  cone 
of  dispersion,  of  which  the  mean  trajectory  constitutes  the  axis. 
Figure  15  shows  a  shrapnel  provided  with  a  time  fuze,  burst- 
ing in  air;  and  figure  16  one  with  an  impact  fuze,  bursting, 
as  it  is  called,  "on  graze." 

The  right  section  of  this  cone  is  circular  and  the  horizontal 
section  elliptical.  The  size  and  form  of  the  ellipse  for  any 
section  vary  with  the  energies  of  the  different  component 
parts,  horizontally  in  the  plane  of  the  trajectory  and  normally 
to  that  plane;  and  also  with  the  sectional  density  of  these 
parts. 


24:  XVI. PROJECTILES. 

The  inevitable  lateral  dispersion  being  sufficient  for  the 
necessary  distribution,  it  is  sought  by  various  means  to 
increase,  at  the  moment  of  their  separation,  the  component 
energy  of  the  parts  in  the  direction  of  the  tangent  to  the 
trajectory.  It  is  to  the  success  of  such  efforts  that  the 
superiority  of  shrapnel  over  case  shot  of  Class  I  is  due. 

Case  shot  are  generally  employed  against  animate  objects, 
a  dangerous  wound  to  which  is  taken  to  correspond  to 
the  energy  required  to  pierce  a  pine  board  one  inch  thick. 
It  is  convenient  to  remember  that  this  requires  a  velocity 
of  about  500  f.  s.  in  an  ounce  ball,  or  to  an  energy  of  about 
one  eighth  of  a  foot-ton.  A  velocity  of  500  f.  s.  is  accordingly 
taken  as  the  limiting  velocity  for  case  shot. 

For  reasons  given,  the  fragments  of  the  envelope  are  in- 
effective as  compared  with  the  members  of  the  cluster,  which 
are  generally  spherical.     The  envelope  is  therefore  made  as 
light  as  possible. 
Structure. 

But  for  the  shock  of  firing,  which  deforms  the  members  of 
the  cluster  even  to  the  extent  of  consolidation,  and  which  may 
even  burst  the  envelope  from  the  dilatation  of  its  contents,  the 
cluster  would  always  be  made  of  lead.  But  lead  is  expensive, 
and  requires  to  be  alloyed  with  tin  or  antimony;  or  to  be  im- 
bedded in  a  matrix  as  of  sulphur  or  rosin;  or  to  be  packe'd 
in  coal  dust  to  resist  this  shock.  Consequently,  iron  is  used, 
except  when  the  conditions  require  every  structural  advan- 
tage to  be  improved. 

Iron  has  the  further  advantage  in  certain  cases  of  making 
the  mean  density  of  the  case  shot  equal  to  that  of  the  shell; 
this  permits  the  firing  to  be  regulated  as  stated  page  4. 

The  size  of  the  balls  depends  upon  the  facility  with  which 
the  envelope  may  be  filled,  upon  the  material  of  which  they 
are  made,  and  upon  the  distance  at  which,  after  separation, 
they  are  required  to  act. 


XVI. — PROJECTILES.     -  25 


CLASS    I.       CANISTER    AND    GRAPE    SHOT. 

These  are  distinguished  by  the  lightness  of  the  envelope, 
which  is  designed  only  for  their  transportation  and  loading. 
The  balls,  generally  of  cast  iron,  are  now  much  smaller 
than  before  shrapnel  attained  its  present  importance. 

Canister. 

For  smooth-bore  cannon  the  envelope  consisted  of  a  tin 
case  supported  in  rear  by  a  disc  which  was  designed  to 
prevent  the  penetration  of  the  gases  into  the  cluster  v^hile 
within  the  bore.  To  avoid  the  rotation  of  the  projectile 
in  rifled  cannon,  the  envelope  is  stiffened  so  as  to  prevent 
its  upsetting  or  dilatation  into  the  rifling.  In  the  English 
service  this  is  done  by  inserting  three  trough-shaped  pieces 
of  sheet  iron  around  the  cluster.  In  the  United  States  service 
a  thin  tube  of  malleable  cast  iron,  closed  at  one  end,  is  em- 
ployed. This  is  known  as  Sawyer's  patent.  The  fragment- 
ation of  this  tube  is  assisted  by  spiral  cuts.     See  figure  17. 

Since  canister  is  retained  only  for  the  extreme  simplicity 
of  its  operation  at  the  short  ranges  at  which  it  is  employed 
by  the  defence,  the  size  of  the  balls  has  been  greatly 
diminished. 

When,  as  in  the  defence  of  the  ditches  of  permanent  works, 
the  desired  eflect  is  not  complicated  by  requiring  projectiles 
of  different  natures  to  be  fired  from  the  same  gun,  canister 
fire  is  replaced  by  that  from  machine  guns.  This  is  continu- 
ous and  does  not  derange  the  aim  so  much. 

Grape  Shot. 

These  were  formerly  employed  in  smooth-bore  guns 
against  both  animate  objects  and  the  masts  and  rigging  of 
vessels.  The  iron  balls  were  arranged  in  tiers  of  three, 
sustained  by  a  central  spindle,  a  top  and  bottom  plate  and 
two  intermediate  rings.  Figure  18.  In  former  times  they 
were  quilted  into  canvas  bags,  whence  the  name. 


26  XVI. — PROJECTILES. 


CLASS  II.     SHRAPNEL. 

Principles  of  Shrapnel. 
Notation. 

Let  V  be  the  initial  velocity  and  v  be  the  remaining  ve- 
locity of  the  shrapnel  at  its  explosion. 

Let  Vy  and  v^^  estimated  respectively  at  right  angles  to,  and 
parallel  to  the  tangent  to  the  trajectory,  be  the  mean  veloci- 
ties of  dispersion  and  of  translation  of  the  N  balls  that  form 
the  sheaf,  irrespective  of  the  velocities  in  these  directions 
that  are  due  to  the  remaining  velocity  v. 

The  velocity  v^^  which  is  taken  without  regard  to  its  sign, 
may  be  due  to  either  or  both  of  two  component  velocities ; 
viz. :  1st.  The  velocity  v^^^  due  only  to  the  bursting  charge; 
and,  2d.  In  oblong  projectiles,  the  velocity  v^^^  due  only  to 
their  rotation. 

The  velocity  v^ ,  which  is  an  increment  of  the  remaining 
velocity,  is  due  only  to  the  bursting  charge,  and  its  sign  de- 
pends upon  the  position  of  the  bursting  charge  within  the 
projectile. 

Tet  v'  be  the  resultant  velocity  of  translation  due  to  z^±  v^, 

Tet  qp  be  the  inclination  to  the  surface  of  the  ground  of 
the  tangent  to  the  trajectory  (the  axis  of  the  cone)  at  the 
point  of  explosion.  It  is  important  to  remember  that,  as 
stated  in  Chapter  I  and  to  be  proved  in  Chapter  XX,  the 
curvature  of  the  trajectory,  or  the  value  of  qp  measured  from 
the  horizon,  is  a  decreasing  function  of  v. 

Let  Q  be  the  angle  at  the  vertex  of  the  cone  of  dispersion, 
figure  24. 

We  will  for  simplicity  suppose  the  cone  to  be  composed  of 
rectilinear  elements,  and  the  surface  of  the  ground  to  be 
horizontal,*  so  that    d  will  be  the  angle  included   between 


*  For  the  effect  of  varying  the  inclination  of  the  ground,  see  Chapter 
XXX,  figure  34. 


XVI. — PROJECTILES.  27 

the  upper  and  lower  tangents  to  the  sheaf  at  its  vertex, 
figure  25. 

Distribution,  t 

It  is  evident  that  the  mean  density  of  the  sheaf  will  be  a 

decreasing  function  of  ^=2  tan-^  —L     Also,  from  the  horizon- 

tal   projection  in  figure   24,    that  since    —     balls    will     be 

found  in  the  area  a  b  o  d,  the  smaller  is  ^,  or  the  more  nearly 
does  the  cone  approach  a  cylinder,  the  more  uniformly  will 
the  balls  be  distributed  over  the  entire  ellipse  a  b  o  d. 

Also,  the  smaller  the  angle  g),  the  greater  is  the  eccen- 
tricity of  the  ellipse ;  or,  for  a  given  lateral  dispersion,  the 
greater  will  be  the  dangerous  space  in  the  line  of  fire. 

N 
If  a  be  the  area  of  the  ellipse,  d=  —  will  be  the  measure 

a 

of  the  density  of  the  section  ;  this  varies  along  the  ellipse ;  see 
figure  24. 

The   shrapnel  will  be  most   effective  when  _  =  —    is  the 

mean  area  occupied  by  one  man  projected  on  the  ground 
by  the  elements  of  the  cone. 

Besides  ^,  g)  and  N  the  value  of  a  will  depend  on  the 
height  above  the  ground,  and  the  distance  in  front  of  the 
target  at  which  explosion  occurs,  or  upon  the  distance  vo=h, 

t  Note.  The  curvature  of  the  axis  of  the  sheaf  causes  the  section  to  be 
not  truly  elliptical,  but  oval  as  in  figure  25.  The  ascent  of  the  balls  in 
the  upper  half  of  the  sheaf,  and  the  curvature  of  their  trajectories  due  to 
their  small  sectional  density,  reduces  their  striking  energy,  so  that  those 
that  fall  near  the  large  end  of  the  oval  are  comparatively  ineffective. 
This  loss  will  be  partly  compensated  for  by  the  ricochet  of  balls  nearer 
to  the  axis,  provided  they  strike  ground  that  is  sufficiently  hard.  For 
ricochet,  the  angle  of  incidence  shonld  be  less  than  20°  :  this  establishes 

a  limiting  value  for  g}  -f"  o  <C^^°. 

These  differences  between  the  actual  and  the  assumed  conditions,  hav- 
ing been  understood,  may,  for  this  discussion,  be  neglected. 


28  XVI. — PROJECTILES. 


Nature  of  Target. 

The  requisites  of  shrapnel  vary  somewhat  with  the  dis- 
position of  the  troops  against  which  it  is  to  be  used.  These 
may  be: 

I.  Either  in  columns  of  manoeuvre,  or  in  deep  masses 
which  it  is  the  object  of  the  artillery  to  force  to  deploy  at 
long  distances.  In  open  ground  these  distances  may  uow  be 
as  great  as  two  miles. 

II.  Deployed  in  line  at  shorter  ranges. 

In  the  first  case,  consistently  with  the  limiting  values  of 

^j  the  values  of  6  and  /i  should  be  small ;    and  conversely  in 

the  second  case.  In  the  first  case,  as  the  enemy  will  gene- 
rally be  in  motion,  and  therefore  erect,  cp  also  should  be  small ; 
and  in  the  second  case,  as  the  enemy  will  generally  be  lying 
down  and  seeking  cover,  cp  also  should  be  large. 

These  conflicting  considerations  require  special  treatment. 
In  the  first  case  guns  with  high  velocities  are  needed,  and  in 
the  second  case  the  limit  will  probably  be  found  in  the  use  of 
field  mortars.  Between  these  limits  guns  may  be  used  with 
reduced  charges  and  at  high  elevations,  and  at  the  closest 
ranges,  say  within  300  yards,  canister  is  most  effective. 

The  two  cases  correspond  to  the  limiting  cases  of  the  cone. 
First,  when  0  =  g)  r=  0.     Second,  when  6  :=z  cp  =z  90"". 

The  first  case,  being  that  most  comprehensive  and  difficult 
to  satisfy,  and  since  it  involves  by  its  opposites  the  second 
case,  is  that  herein  discussed. 

Choice  of  Fuze. 

Shrapnel  may  be  exploded  in  the  two  ways  shown  in  fig- 
ure 16,  viz.,  "  on  graze  "  by  an  automatic  impact  fuze,  or  in 
the  air  by  an  adjustable  time  fuze.  These  have  different 
spheres  of  action  as  follows : 

Impact  fuzes  may  be  used  at  short  ranges  where  v  is  large 


XVI. — PROJECTILES.  29 


and  0  and  cp  are  therefore  small;  and  where  q'  the  angle  of 
reflexion  (always  greater  than  9),  is  also  small.    Figure  16. 

But  they  act  irregularly  when  the  ground  is  soft  or  rolling ; 
and  at  long  ranges  when  v  is  small  and  9  is  large,  the  energy 
lost  on  impact  reduces  the  already  diminished  value  of  v, 
and  consequently  increases  the  value  of  6,  The  time  fuze 
is  therefore  essential  for  soft  or  rolling  ground,  and  for  long 
ranges  over  any  ground.  A  possible  objection  to  it  applies 
to  the  risk  attending  its  premature  discharge  when  firing  over 
friendly  troops. 

On  some  accounts  the  time  fuze  is  less  well  adapted  for  use 
at  short  ranges  than  is  the  impact  fuze ;  since  for  a  given 
error  in  the  time  of  its  burning,*  the  greater  is  z',  the  greater 
will  be  the  resulting  variation  in  h,  and  therefore,  for  given 
values  of  6  and  qp,  the  greater  will  be  the  variation  in  a. 

Although  this  objection  is  partly  neutralized  by  the  small 
values  of  6  and  (jp  at  short  ranges,  the  conditions  seem  to  re- 
quire the  use  of  two  fuzes  in  each  projectile.  See  the  co7n- 
bination  fiize^  Chapter  XVIII.  Meanwhile  the  improvement 
of  the  time  fuze  is  one  of  the  most  important  problems  in 
ordnance. 

Computing  the  Value  of  d  for  Rifled  Shrapnel. 

Let  p  be  the  mean  radial  distance  of  the  balls. 

This  is  taken  instead  of  the  radial  distance  of  the  outer 
ball,  as  is  generally  done,  since  the  distribution  of  the  balls 
throughout  the  cross  section  of  the  sheaf  is  more  important 
than  their  extreme  lateral  dispersion. 

Let  r  be  the  external  radius  of  the  shrapnel,  taken  equal 
to  that  of  the  bore  of  the  gun. 

Although  Fwil  be  reduced  during  flight,  it  is  assumed, 
and   experiment  confirms  the  assumption,   that   at  ordinary 


*  The  mean  error  (Chapter  XXX,  page  24)  in  the  time  of  burning  may 
be  taken  as  about  0.05  sec. 


80  XVI. — PROJECTILES. 


ranges  the  angular  velocity  of  the  projectile  does  not  sensibly 
diminish.* 

Under  this  assumption,  from  Equations  (2)  and  (3)  the  tan- 
gential velocity  of  the  mean  ball  will  be  nearly 

P"  =  ;~^.  (5) 

and,  since  we  are  considering  only  the  tangential  velocity  due 

to  rotation,  we  have  Vjy  =  p  cj  and 

6       p  0)      pn  F  . -. 

tan  -  =  '-J-  =  "^ ,.  (6) 

If  we  substitute  in  this  equation  the  empirical  value  of  n  in 
Equation  (4)  we  have, 

tan-=-y--^,  (7) 

and  for  a  given  shrapnel  in  which  V^  n,  and  -  are  known, 

tan|=|;  (8) 

an  equation  easily  remembered,  and  which  agrees  fairly  well 
with  practice. 

History. 

The  history  of  the  improvement  of  shrapnel,  which  is  now 
the  principal  field  artillery  projectile,  illustrates  many  impor- 
tant principles.      As  stated,   page   24,  improvements   liave 

tended  to  reduce  the  ratio  -~- ,  and  to  increase  the  sectional 

7/ 

density  of  the  projectile  as  a  whole,  and  that  of  the  balls  it 
contains. 

Spherical  Shrapnel, 

I.  Shrapnel,  as  invented  in  1808,  by  General  Shrapnel  of 
the  British  service,  were  simply  spherical  shell,  loaded  loosely 
with  musket  balls  and  a  bursting  charge. 


*  Projectiles  fired  vertically  upward  have  returned  to  the  earth  with 
sufiicient  rotation  to  keep  them  point  foremost. 


XVt. — PROJECTILES.  SI 


In  transportation  the  powder  was  triturated  by  the  balls, 
and  on  firing  the  piece  the  shock  might  cause  a  premature 
explosion,  or  might  conglomerate  the  balls ;  sometimes  even 
.causing  the  projectile  to  be  ruptured  by  the  resulting  dilation 
of  the  cluster.  The  ignition  of  the  bursting  charge  at  the 
proper  time  was  also  uncertain. 

In  order  to  make  F  large  enough  to  give  a  large  value  to 
Z',  the  walls  of  the  shell  were  made  thick  enough  to  stand  a 
heavy  propelling  charge.  But  this  diminished  the  value  of 
N^  and,  since  the  interstitial  volume  between  the  balls  was 
large,  7u  had  to  be  made  large  in  order  to  obtain  sufficient 
pressure  to  burst  the  shell.  The  energy  remaining  in  the 
powder  gases  after  rupture  of  the  walls  being  large,  the  balls 
were  widely  scattered,  making  7>y  large.     The  resultant  value 

of  vx   was  zero.     At  long  ranges,  tan  -  =    -^    was  there- 
fore  large. 

2.  The  next  step  was  the  invention  of  spherical  case,  much 
used  during  our  civil  war. 

By  imbedding  the  balls  in  melted  sulphur  and  boring  out  a 
chamber  for  the  bursting  charge,  figure  19,  the  value  of  iv 
could  be  decreased,  and  the  certainty  of  its  ignition  at  the 
proper  time  be  increased.  The  matrix  supported  the  walls  in 
firing,  so  that  their  thickness  could  be  decreased  and  N  be 
increased.  But  the  matrix  often  retained  the  balls  after  ex- 
plosion, and  the  value  of  7^x  was  still  zero. 

3.  Colonel  Boxer,  of  the  Enghsh  army,  devised  a  shrap- 
nel, figure  20,  in  which  the  balls,  hardened  by  an  alloy  of 
antimony,  and  packed  in  coal  dust,  were  separated  from  the 
bursting  charge  by  a  wrought  iron  diaphragm  around  which 
the  envelope  was  cast.  The  seat  of  the  diaphragm  and  sev- 
eral other  meridional  grooves  served  to  weaken  the  envelope 
and  to  diminish  the  value  of  w. 

While  the  projectile  was  necessarily  fired  with  the  fuze  in 


32  XVI. — PROJECTILES. 


front,  the  non-coincidence  of  the  centers  of  figure  and  of 
mass  caused  the  resistance  of  the  air  to  turn  the  Hghter 
portion  of  the  projectile  to  the  rear,  so  that  z^x  was  always 
positive. 

This  projectile  marked  the  farthest  advance  of  spherical 
shrapnel. 

Oblong  Shrapnel. 

The  advantages  of  the  oblong  form  of  shrapnel  are  as 
follows : 

It  permits  the  base  of  the  envelope  to  be  strengthened 
without  increasing  the  thickness  of  the  walls.  This,  with  im- 
provements in  cannon  and  gunpowder,  has  increased  the 
value  of  Vj  and  since  the  sectional  density  has  been  increased 
so  that  at  long  ranges  ^  has  been  diminished,  it  has  also  in- 
creased the  eccentricity  of  the  section  of  the  cone  of  disper- 
sion by  the  ground.  By  placing  the  bursting  charge  in  rear, 
Z'x  has  become  positive,  and  z'yb  has  become  practically  zero. 

An  example  of  such  a  projectile  is  seen  in  figure  21,  in 
which  B^  is  the  cast  iron  body  ;  H,  the  ogival  head  of  wood, 
covered  with  a  sheet  iron  cap  by  which  it  is  riveted  to  B  ; 
C,  the  powder  chamber,  made  conical  to  facilitate  unloading; 
Z>,  a  disc  by  which  the  cluster  is  swept  out  to  the  front;  T,  a 
tube  to  carry  the  flame  from  the  fuze,  7%  to  C.  A  paper  lining 
keeps  the  rosin  matrix  from  adhering  to  the  walls  of  the  cavity. 

The  shght  resistance  of  the  attachments  of  the  head  makes 
of  this  projectile  a  sort  of  aerial  gun. 

The  objections  to  this  projectile  indicate  the  nature  of  re- 
cent improvements.  The  wooden  head,  the  tube,  the  disc, 
and  the  thickness  of  the  walls  required  by  the  nature  of  cast 
iron,  diminish  JV  so  much,  that  the  balls  form  about  one- 
quarter  the  weight  of  the  whole  projectile. 

The  bursting  charge  is  too  small  to  produce  sufficient 
smoke  to  indicate  the  explosion  at  distant  ranges,  and  thereby 
to  assist  in  correcting  the  aim. 


XVI. PROJECTILES. 


The  position  of  the  bursting  charge  is  such  that,  while 
acting  well  in  air,  when  used  with  an  impact  fuze  the  delay- 
caused  by  the  passage  of  the  flame  through  the  tube  causes 
the  projectile  to  rise  too  high  before  bursting. 

Present  Practice. 

The  most  recent  ideas  on  the  subject  are  embodied  in 
figures  22,  23. 

Figure  22  contains   a  combined  time  and  impact  fuze. 

The  bursting  charge  is  situated  in  front,  occupying  the 
room  which  in  figure  21  is  wasted.  It  is  large  enough  to 
give  the  smallest  volume  of  smoke  visible  at  extreme  ranges. 

The  envelope  consists  of  a  thin  drawn  steel  tube,  secured 
in  rear  to  a  separate  base,  and  slit  and  compressed  in  front  to 
an  ogival  form. 

The  cluster  consists  of  a  column  of  leaden  balls,  separated 
by  discs  of  cast  iron.  The  discs  are  sunken  to  fit  the  balls, 
and  form  a  skeleton  matrix. 

When  the  bursting  charge  explodes,  the  slit  ends  of  the 
point  are  thrown  back,  so  as  to  dirhinish  the  sectional  density 
of  the  envelope  as  compared  with  that  of  the  cluster. 

The  latter  moves  on  with  v'  z=.v  —  v^  =v  —  about  200/.  s. 

Figure  23  represents  a  more  recent  form,  of  which  in  1891 
a  number  are  in  process  of  manufacture  for  experimental  trial. 

Its  construction  is  apparent.  The  tube  is  of  thin  brass, 
enlarging  its  capacity  for  powder,  and  facilitating  the  passage 
of  the  flame  from  the  fuze.  The  w^alls  are  weakened  by 
longitudinal  grooves.  It  remains  to  be  seen  whether,  com- 
pared with  figure  22,  the  increase  in  7'yb  resulting  from  this 
construction  will  not  neutralize  the  increase  in  Vyr^ , 

THE    SEGMENT    SHELL. 

An  attempt  was  made  some  years  ago  to  combine  the 
functions  of  solid  shot,  shell  and  shrapnell  in  the  segment 
shell,  in  which  the  cluster  was  composed  of  the  sectors  of 


S4  XVI. — PROJECTILES. 


concentric  cylinders  arranged  so  as  to  form  a  solid  mass. 
But  such  a  violation  of  the  principle  of  the  independe^ice  of 
function^  which  requires  that  where  simplicity  permits,  eacli 
specific  function  be  separately  provided  for,  necessarily 
failed.  The  importance  of  this  principle  in  the  design  of 
machines  of  all  kinds  can  hardly  be  too  forcibly  stated.  The 
opposite  of  this  idea,  that  of  combination,  by  which  more 
than  one  office  or  function  is  expected  of  any  one  member 
of  the  machine  or  organization,  is  seldom  found  to  be  com- 
patible with  the  efficiency  of  the  whole,  as  we  shall  have 
many  opportunities  of  seeing  during  this  course.  The  full 
development  of  the  principle  of  the  independence  of  function 
leads  naturally  to  complication  or  the  multiplication  of  parts; 
judgment  is  therefore  required  to  compromise  between  sim- 
plicity and  efficiency.  The  history  of  invention  appears  to 
indicate  the  pre-eminence  of  efficiency. 

As  a  case  in  point,  it  is  now  conceded  that  three  types  of 
the  two  classes  of  projectiles  are  required  for  field  and  siege 
artillery;  viz.:  shell,  to  convey  kinetic  energy  for  penetration, 
and  potential  energy  for  demolition  and  moral  effect;  and 
case  shot  for  kinetic  energy  only.  Although  shrapnel,  when 
reversed  in  the  gun,  may  in  an  emergency  replace  canister; 
it  is  better  to  carry  a  few  rounds  of  the  latter,  preferably, 
as  in  the  British  service,  on  the  carriage  which  supports  the 
piece. 

REGULATING    SHRAPNEL    FIRE. 

Referring  to  figure  24  we  may  consider  the  horizontal  and 
vertical  projections  of  //,  viz.,  x  —  h  cos  cp  ;  j^  =  A  sin  gi. 

Of  these  quantities,  which  are  separately  discussed  in  the 
regulation  of  fire,  x  is  mainly  varied  by  changing  the  time  of 
burning  ;  and  y  by  changing  the  angle  of  fire. 

Under  given  conditions  x  varies  inversely  as  the  range. 
Its  variations,  however,  are  not  great,  since  there  are  com- 
pensations that  tend  to  keep  it  constant.     It  is  found  that 


XVI. PROJECTILES.  35 


the  best  results  follow  a  value  of  j\;  =  50  yards  for  all  dis- 
tances except  those  very  short,  for  which  x  may  increase  up 
to  100  yards.  If  x  be  taken  too  small,  too  great  a  propor- 
tion of  the  shrapnel  fired  will  explode  beyond  the  target  and 
be  wholly  lost. 

In  order  to  utilize  the  small  values  of  qp  in  the  upper  half 
of  the  sheaf,  it  is  advisable  to  make  y  small.  It  is  found 
that  the  best  results  follow  a  value  of  y  varying  from  2  yards 
at  500  yards  range,  to  6  yards  at  2,500  yards  range.  Greater 
values  of  y  are  not  used,  since  they  are  difficult  to  observe 
correctly  at  long  distances.  The  reason  for  the  increase  of  ji^ 
is  due  to  the  increase  of  cp  at  long  ranges,  and  the  consequent 
decrease  in  the  area  of  the  section  cut  from  the  cone  by  the 
surface  of  the  ground. 

These  rules  are  in  the  nature  of  approximations.  In  prac- 
tice the  fire  is  regulated  by  signals  from  observers,  placed  as 
far  as  possible  to  the  front  and  flank. 

EMPLOYMENT  OF  FIELD  PROJECTILES. 

Shells. 

These  projectiles  when  used  with  a  time  fuze  would  follow 
the  principles  laid  down  for  shrapnel ;  but  the  large  value  of 
6  and  the  small  value  of  N  would  make  this  unprofitable. 

They  accordingly  use  an  impact  fuze,  which  makes  of  them 
the  best  means  of  controlling  elevations.  See  page  4,  and 
Chapter  XXX,  page  20. 

They  are  generally  used  against  inanimate  objects  to  be 
demolished,  pierced  or  set  on  fire. 

In  the  following  cases  they  may  be  used  against  troops  : 

1.  At  distances  too  great  for  the  time  fuze. 

2.  When  the  enemy  is  hidden  in  a  village,  or  in  thick 
woods. 

The  violence  of  their  explosion  assists  their  moral  effect, 
particularly  against  horses  and  fugitive  masses. 


36  XVI. PROJECTILES. 


Shrapnel. 

These  are  exclusively  used  against  animate  objects  in  the 
open,  or  in  thin  cover.  They  were  found  very  destructive  in 
the  Russo-Turkish  war.  In  siege  oper  ttions  they  serve  to 
annoy  parties  working  at  night  to  repair  the  damages  done 
by  day. 

PENETRATION  OF  ARMOR. 
General  Considerations. 

The  penetration  of  armor  depends  principally — 

I.  Upon  the  nature  of  the  armor.  In  the  order  of  resist- 
ance armor  may  be  classed  as  follows : 

Cast  iron  with  a  chilled  face,  used  only  for  land  defenses 
and  not  considered  herein. 

Steely  forged  and  tempered. 

Compound^  viz.,  a  wrought-iron  back  with  a  hard  steel 
face. 

Wrought  iron^  now  obsolete. 

Roughly  speaking,  armor  yields  either  by  ptinching  or 
racking.  In  the  first  case,  as  in  wrought  iron,  the  effect  is 
local.  In  the  second  case,  the  energy  of  impact  is  distrib- 
uted throughout  a  greater  mass  of  the  plate  and  tends  to 
crack  the  plate  or  to  wrench  it  from  its  fastenings.  The  effect 
is  mainly  to  remove  an  obstacle  to  further  penetration.  Cast 
iron  armor  yields  in  this  way,  and  so  do  steel  armor  and  the 
face  of  compound  armor  if  too  brittle. 

The  object  of  the  artillerist  is  to  concentrate  energy  on  a 
small  area,  so  as  to  reach  the  objects  which  the  armor  is  in- 
tended to  protect,  /.  e.,  to  punch. 

The  object  of  ihe  armor-maker  is  to  protect  these  objects, 
by  distributing  the  energy  of  impact  as  much  as  possible 
between  the  projectile  and  the  mass  of  the  plate,  so  that  even 
at  the  risk  of  destroying  the  plate  by  racking,  the  shot  must  be 
kept  out. 


XVI. — Projectiles.  87 


But  if  racking  can  be  avoided  without  loss  of  resistance  to 
punching,  the  quahty  of  the  plate  is  improved.  In  the  early- 
manufacture  of  armor,  racking  effects  predominated ;  these 
disappeared  as  its  manufacture  was  improved  ;  while  the  resist- 
ance to  punching  was  maintained  or  even  increased.  For  ex- 
ample, the  principal  objection  to  steel,  for  armor  as  for  other 
purposes,  has  been  its  brittleness.  But  at  Annapolis,  in  1890, 
carbon  steel  armor  resisted  punching,  but  was  slightly  racked. 
Nickel  steel  armor  resisted  both  racking  and  punching.  Com- 
pound armor  failed  in  both  respects. 

The  nature  of  the  backing  or  support  against  which  the 
plate  rests,  considerably  affects  its  resistance.  Except  for 
compound  armor,  for  which  the  backing  cannot  be  too  rigid, 
the  backing  should  be  somewhat  elastic,  so  as  to  absorb 
energy,  after  the  manner  of  a  cushion  supporting  a  board  in 
which  one  seeks  to  drive  a  nail. 

As  the  liability  to  racking  increases,  the  number  of  the 
bolts  by  which  the  armor  is  held  in  place  should  also  increase, 
so  as  to  retain  those  portions  which  would  otherwise  be 
displaced. 

II.  As  a  consequence  of  the  above  must  be  considered 
the  resistance  of  the  projectile  to  permanent  deformation ; 
page  3. 

III.  Upon  the  striking  energy  of  the  projectile,  measured 
in  a  direction  normal  to  the  plate. 

Since  the  projectile  acts  after  the  manner  of  a  punch, 
shearing  its  way  through  the  plate,  the  energy  is  often 
estimated  per  unit  of  circumference.  In  earth  and  masonry, 
in  which  the  material  is  soft,  the  projectile  is  supposed  to 
compress  it  to  the  front,  and  the  energy  is  taken  per  unit  of 
area  of  cross  section.^ 

*  As  experience  with  plates  and  projectiles  of  varying  resistance  to  per- 
manent deformation,  increases,  such  assumptions  are  gradually  replaced 
by  purel)  empirical  formulae  suited  to  each  special  case. 


J^8  XVI.— PROJECTILES. 


Whereas  in  experimental  tests  normal  impact  is  the  rule,  in 
firing  at  ships  it  will  be  the  exception.  The  shape  of  the 
point  of  the  projectile  also  tends  to  make  it  glance,  so  that 
for  these  reasons  armored  ships  may  be  expected  to  resist 
more  than  the  formulae  predict. 

Haitian d's  Formula  of  1880.* 

The  energy  expended  in  other  forms  than  in  perforation, 
as  in  heating  the  plate  and  projectile,  and  in  deforming  the 
latter,  has  given  rise  to  many  empirical  formulae,  some  of  which 
may  be  found  in  the  Course  of  Permanent  Fortification.  A 
very  successful  formula,  Froloff''s^  assumes  that -the  energy  so 
lost  is  proportional  to  the  striking  velocity,  so  that  the  pene- 
tration is  proportional  to  the  momentum  of  the  projectile  on 
impact.  The  following  formula,  which  illustrates  a  principle 
already  taught,  is  considered  by  recent  writers  to  be  one  of 
the  best     Equation  (15). 

Let  t  be  the  thickness  in  inches,  of  wrought  iron  armor  that 
would  just  be  perforated  by  a  cast  iron  projectile,  whose 
weight  is  W^  its  normal  velocity  on  impact  v^  and  its  diam- 
eter d. 

Let  e  be  the  normal  energy  in  foot-tons,  or  ^  =  tt— s?r<7r 
^^  2^^  2240  . 

Let  s  be  the  energy  in  foot-tons  per  inch  of  circum- 
ference, or  f  =  =- . 

TT  a 

During  a  prolonged  series  of  experiments  made  by  Colonel 
Maitland  it  was  found — 

1st.  That  /  varied  directly  with  £,  or 

'=/(■?)■         « 

*  It  is  inferred  that  the  experiments  on  which  Maitland's  formula  is 
based  were  made  with  ordinary  cast  iron  projectiles,  and  that  the  armor 
was  backed. 


XVI— I^ROJECTILES.  80 


2nd.  It  was  also  observed  that  when  projectiles  of  different 
calibers  were  arranged  in  classes  according  to  their  spherical 
densities;  in  each  class  the  penetration  measured  in  calibers 
was  very  nearly  proportional  to  the  striking  velocity. 

For  a  particular  class,  known  as  the  standard  projectiles,  of 
which  the  spherical  density  was  3.0,  the  penetration  was  nearly 
one  caliber  for  every  thousand  feet  of  striking  velocity.  This 
is  known  as  Captain  Orde-Browns  *'  rule  of  thumb." 

For  purposes  of  comparison,  let  us  assume  a  given  gun  to 
be  fired  against  a  given  plate  ;  d  and  /  will  then  be  constant, 
and  the  variation  in  spherical  density  will  result  from  varying 
the  weight  of  the  projectile.  The  variables  will  then  be  W 
and  V.  For  the  standard  projectiles  let  these  be  represented 
by  W,  and  v^, 

Owing  to  the  number  of  experiments  made  with  the  stand- 
ard projectiles,  special  weight  is  given  to  the  results  obtained 
from  them.  These  results  are  expressed  in  the  following 
general  formula,  differing  slightly   from    Orde-Brown's  rule, 

viz. :  «  =  ISOO  -  *^-^^-  (^"> 

To  pass  from  standard  projectiles  to  those  not  standard, 
we  use  Equation  (9)  in  order  to  ascertain  the  relation  between 
V,  and  V,     Under  the  hypothesis  that  d  and  /  are  constant  it 

becomes  v  ^  f  y\j ^  '       (11) 

Whence  v\v\\  Jw  :  y/W„  or  z;  =  v  \/^.  (12) 

In  the  standard  projectiles,  J^=  0.375  ^/^ ;  whence,  from 
Equation  (11)  ,,  =  1^^^^W^  (13) 

Substituting  in  Equation  (10)  we  have 


40  XVI. — PROJECTILES. 


Y/f__0.14;  (14) 


"-  612.4  d 
Whence,  multiplying  both  members  by  d^ 

'="'^=  ski  \/f-- 0.14^.  (15) 

The  value,  /,  thus  obtained  is  the  thickness  of  a  plate  that 
will  just  be  perforated  by  a  projectile  having  an  ogival  head 
with  a  radius  of  curvature  of  1.5  calibers.  If  the  radius  of 
curvature  is  increased  to  2  calibers,  as  is  now  customary,  t 
will  be  increased  by  5  or  10  per  cent,  and  Orde-Brovvn's  rule 
will  increase  in  exactitude. 

If  the  plate  resists  perforation,  then  the  penetration  may 
be  taken  as  about  0.9  of  the  estimated  perforation. 

The  Formulae  of  De  Marre. 

The  following  formulae  result  from  recent  experiments  in 
France  and,  except  for  Equation  (20),  cover  a  great  range  in 

calibers,  and  in  the  ratio  - . 
d 

In  the  English  units  previously  used  we  have  for  modern 

projectiles,  viz.,  chilled  iron  shot  and  steel  shells. 

I.  For  the  perforation  of  wooden  backing  when  used  as 
such,  i.  e.,  not  unprotected 

^b  =  0.1823  /  ^-^  ^  ••«  (16) 

This  is  about  70  per  cent  greater  than  when  the  backing  is 
unprotected. 

II.  For  a  wrought  iron  armor  plate  that  is  hacked ;  the 
resistance  of  the  plate  alone  being  considered 

^j  =  5.809 /^-V-^  (17) 

Owing  to  the  improvement  of  projectiles  since  1880  this 
is  less  than  the  value  implied  by  Equation  (15). 


XVI. — PROJECTILES.  41 


For  the  entire  target  consisting  ot  the  plate  and  backing 

^i  =  ^i  +  ^b.  a8) 

III.  For  the  rather  soft  steel  plates^  generally  used  for  heavy- 
armor,  as  made  at  Creusot,  when  backed 

^3  =  7.286  Z'-*^'-"*  (19) 

See  also  Equation  (18). 

IV.  For  the  thin  plates  of  hard  steel,  unbacked,  used  for  gun 
shields,  when  attacked  by  the  comparatively  small  cannon 
known  as  Rapid- Fire  guns  and  Revolving  Cannon 

^p  =  12.86 /'-^^'-^  (20) 

These  formulae,  while  abundantly  verified  in  the  French 
service,  must  be  accepted  with  caution  when  the  conditions 
differ  from  those  under  which  they  were  deduced. 

Very's  Formula. 

Mr.  E.  W.  Very,  formerly  of  the  U.  S.  Navy,  has  recently 
proposed  a  means  of  comparing  the  resistance  of  steel  plates 
that  has  long  been  desired,  since  it  eliminates  variables 
relating  to  the  nature  of  the  plate,  its  thickness  and  the  cali- 
ber and  velocity  of  the  projectile,  all  of  which  may  differ  in 
experiments  made  at  different  times  and  places. 

It  assumes  that  the  projectile  is  not  deformed,  and  that  no 
other  effect  is  produced  but  that  of  punching,  which  is  sup- 
posed to  be  complete.  The  effect  is  referred  to  that  pro- 
duced in  wrought  iron,  since  withm  ordinary  limits  all  such 
armor  is  homogeneous,  and  is  therefore,  well  adapted  for  use 
as  a  standard  of  comparison. 

Suppose  we  find  by  trial  that  a  certain  projectile  will  just 
perforate  a  given  steel  or  compound  plate  with  a  certain 
energy  e^.  Calculate  the  energy  e^  required  for  the  same  pro- 
jectile to  perforate  a  wrought  iron  plate  of  the  same  thickness, 

e 
and  similarly  backed.     Then  -1  z=  g),  m  which  qp  is  a  factor 


42  XVI. — PROJECTILES. 


expressing  the  relative  per  cent  of  energy   required  to  per- 

2140 
forate  the  steel  plate,  e,  g.  ^-—  —  107  per  cent. 

Since  1880  the  improvement  in  projectiles  has  been  so 
great  that  e^  has  decreased  considerably.  Improvements  in 
the  quality  of  steel  armor  have  increased  e^,  so  that  (p  has  in- 
creased from  about  125  to  over  150.     See  next  topic. 

Weaver's  Formula. 

It  has  long  been  thought  that  besides  its  thickness,  the  mass 
of  the  plate  affects  its  resistance  to  penetration,  and  conse- 
quently the  '■^  energy  per  ton  of  plate^''  is  often  recorded  in  the 
reports  of  firing  against  armor.  No  use  is  known  to  have 
been  made  of  this  knowledge,  however,  until  the  following 
formula,  proposed  by  Lieut.  Weaver  of  the  U.  S.  Artillery. 

•  It  is  probable  that  the  work  is  practically  confined  to  a 
mass  of  some  definite  volume  immediately  surrounding  the 
point  of  impact,  and  that  the  volume  of  this  mass  is  a  cylin- 
der, the  diameter  of  which  is  n  times  the  diameter,  d^  of  the 
projectile,  and  the  height  of  which  is  /,  the  thickness  of  the 
plate. 

Experiments  show  that  a  notable  increase  in  temperature 
and  the  bulge  are  confined  to  a  tolerably  distinct  ring,  about 
2  calibers  wide,  so  that  n  is  probably  not  less  than  5.  It  is 
probable  also  that  it  is  safe  to  allow  for  an  exterior  ring  which 
absorbs  part  of  the  energy,  although  the  effects  in  this  ring 
are  not  apparent.  The  value  of  7i  also  depends  upon  the 
relation  between  t,  the  thickness  of  the  plate,  and  d,  the 
diameter  of  the  projectile.  Lieut.  Weaver  expresses  this  re- 
lation for  Creusot  steel  by 

n  =  6.25  +  0.22  (/  —  d)  (21) 

in  which  /  and  d  are  in  inches.  This  value  will  depend  upon 
the  rigidity  of  the  material,  and  is  subject  to  correction  by 
experiment. 


XVI. PROJECTILES.  43 


In  wrought  iron  n  will  approach  unity,  as  the  effect  is 
noticeably  local  and  no  great  increase  of  temperature  in  the 
adjacent  parts  is  observed. 

From  a  general  consideration  of  records  Lieutenant  Weaver 
finds  that  about  1828  foot  tons  of  energy  per  ton  of  plate  is 
necessary  to  perforate  the  entire  target,  consisting  of  a  steel 
armor  plate  and  its  backing.  This  assumes  the  plates  to  be 
substantially  uniform  in  resistance,  the  projectile  to  be  inde- 
formable,  and  neglects  secondary  effects,  such  as  racking. 
Calling  this  coefficient,  C ;  the  weiglit  in  tons  of  the  disc  in 
question,  W^\  and  the  weight  in  tons  of  one  cubic  inch  of 
the  plate,  w;  he  writes  : 

£.=  ff/,C=(«-'^)%/.^C  (22) 

Supposing  w  —  log  ~^  4.1028  and  substituting  for  tt,  w  and 
C  their  values,  we  have  the  general  formula 

A  =  0.1828  ie  d^  t  (23) 

APPLICATION. 

We  may  now  compare  the  foregoing  formulae  by  reference 
to  the  experiments  at  Annapolis  in  September,  1890.  The 
plates  were  10.5  inches  thick,  backed  by  36  inches  of  oak, 
and  were  fired  at  by  steel  shells,  as  follows : 

No.  of     fT-    ■■  ,  TT^       Spher.  Effect  on 

shots.      ^^^"^-  '^  ^^       Dens.       ^  '  Projectiles. 

8  Holtzer  Steel,  6  in.  100  lbs.  3.70  2075  2988  6  unbroken. 

2  Firminy  "       8  "     210  "     3.28  1850  4988  2  broken. 

Confining  our  attention  to  the  unbroken  6  inch  projectiles, 
only  the  points  of  which  perforated  the  carbon  and  nickel 
steel  plates,  Lieutenant  Weaver's  formula  gives  ^g  =  362 L 
If  from  this  we  subtract  e^  =  77,  per  Equation  (16),  we  have 
e^  =  3544,  which  is  18  per  cent  more  energy  than  the  plates 
received  from  any  one  blow.  As  the  plates  were  not  com  ■ 
plete^   perforated,  this   would    indicate   that   the  value   of 


44  XVI. — PROJECTILES. 


(p  z=  195  from  Equations  (18,  21)  is  more  nearly  correct  than 
that  of  (p  =  158  assigned  by  Mr.  Very's  method ;  viz.,  by 
dividing  2988  X  100  by  the  vaUie  of  c,  =  1816,  given  by 
Equation  (18). 

ROCKETS. 

Definition. 

A  rocket  is  a  projectile  propelled  by  a  source  of  energy 
which  it  contains ;  it  therefore  performs  also  the  functions  of 
a  cannon. 

Structure. 

A  rocket  consists  of  a  cylindrical  case  of  paper  or  metal, 
containing  a  composition  formed  of  the  ingredients  of  gun- 
powder mixed  in  suitable  proportions.  The  front  end  of  the 
case  is  usually  closed,  but  the  other  end  contains  one  or  more 
holes  or  vents  for  the  escape  of  gas  from  the  ignited  compo- 
sition. Within  the  rocket  is  a  hollow  space  called  the  bore ; 
this  may  be  formed  by  driving  the  composition  around  a 
spindle  which  is  afterwards  withdrawn ;  or  by  boring  out  the 
composition  after  its  compression  to  a  solid  state. 

The  case  is  surmounted  by  a  pointed  head,  which,  for 
signal  rockets,  consists  of  a  hollow  paper  cone,  and  for  mil- 
itary rockets  of  any  suitable  projectile  Depending  upon 
the  particular  system  of  construction,  some  means  is  also 
provided  for  guiding  the  rocket  in  its  flight. 

Composition. 
Since  the  composition  is  required  to  ignite  readily,  and 
since  the  amount  of  fouling  is  not  objectionable,  the  pro- 
portion of  sulphur  is  increased;  and,  since  the  gradual 
evolution  of  a  large  volume  of  gas  rather  than  a  large 
amount  of  heat  is  required,  the  proportion  of  nitre  is  dimin- 
ished, while  that  of  charcoal  is  increased,  so  as  to  yield  CO 
rather  than  CO,.  To  further  delay  the  combustion  the  in- 
gredients are  often  mixed,  rather  than  incorporated. 


XVI. — PROJECTILES.  45 


Bore. 

The  bore  is  necessary  to  provide  a  large  surface  of  initial 
combustion.  In  order  to  maintain  a  uniform  pressure 
throughout  the  flight  and  so  avoid  either  excessive  strength 
and  weight  of  the  case  when,  at  first,  the  pressure  is  low; 
or  a  deficiency  of  strength  when,  by  the  increase  of  the 
surface,  the  pressure  increases,  the  composition  should  burn 
on  a  surface  which  is  nearly  uniform. 

To  prevent  its  burning  on  a  decreasing  surface,  the  com- 
position must  be  so  tightly  packed  within  the  case  that  the 
flame  cannot  pass  around  it. 

The  conical  form  increases  the  initial  surface  without 
increasing  either  of  the  above  objections.  Jt  also  facilitates 
the  withdrawal  of  the  spindle  and  increases  the  strength  of 
the  composition  at  the  section  corresponding  to  the  immov- 
able layer  in  a  gun.     Chapter  VII,  page  1. 

Vent. 

The  momentum  of  the  rocket  is  proportional  to  that  of 
the  escaping  gas.  The  velocity  of  the  gas  will  increase  with 
the  pressure,  and  this  will  increase  as  the  size  of  the  vent 
diminishes.  The  longitudinal  and  the  cross  sections  of  the 
vent  must  be  so  chosen  that  the  gas  will  escape  as  fast  as  it  is 
formed,  or  nearly  so,  otherwise  the  velocity  of  the  rocket 
will  be  diminished  and  it  may  burst.  See  Chapter  XI, 
page  8. 

The  excess  of  the  total  pressure  on  the  head  of  the  bore 
over  that  on  the  base,  and  the  diminishing  mass  of  the 
composition  accelerate  the  motion  of  the  rocket  until  the 
resistance  of  the  air  is  equal  to  the  propelling  pressure:  the 
variation  in  velocity  will  then  be  slight.  When  the  gas 
ceases  to  flow  the  rocket  becomes  an  ordinary  projectile. 

Guiding  Principle. 

The  propelling  force  of  the  gas  acts  always  in  the  direc- 
tion of  the  axis  of  the  bore;  it  follows,  therefore,  that  with- 


46  XVI. — PROJECTILES. 

out  some  means  of  'giving  stability  to  this  axis,  the  path 
described  will  be  very  irregular;  so  much  so  at  times  as  to 
fold  upon  itself.  Instances  have  been  known  when  rockets 
have  returned  to  the  point  from  which  they  started.  Stead- 
iness of  flight  is  obtained  either  by  a  guide  stick,  or  by 
rotation. 

The  guide  stick  is  used  for  signal  rockets.  It  consists  of 
a  long  wooden  stick  affixed  to  the  case  so  as  to  bring  the 
center  of  atmospheric  pressure  well  in  rear  of  the  center 
of  gravity.  Any  tendency  to  deflection  is  resisted  by  the 
atmospheric  moment. 

The  Hale  rocket,  figure  26,  owes  its  stability  to  rotation 
produced  by  the  escaping  gas.  As  this  expands  on  escaping 
through  the  vents,  it  presses  against  the  concentric y^<?;?<r^i-,  F^ 
partly  surrounding  each  of  the  three  vents,  and  so  causes 
rotation. 

The  effect  is  increased  in  Macdonald's  Hale  rocket  by  a 
similiar   arrangement   in   front.     In  this   rocket  the  bore 
extends  throughout  the  composition. 
General  Remarks. 

The  difficulties  found  in  constructing  rockets  so  as  to 
prevent  the  shrinking  of  the  composition  from  the  walls  of 
its  envelope;  their  inaccuracy,  and  their  low  capacity  as 
vehicles  of  kinetic  energy  have  limited  their  use  m  recent 
times  to  incendiary  purposes,  particularly  in  savage  warfare. 
Where  transportation  is  difficult  and  the  enemy  dwells  in 
huts  of  an  inflammable  nature,  as  in  Africa,  the  portability 
of  these  weapons  causes  them  still  to  be  retained  by  the 
British  service. 

Rockets  are  also  much  used  for  transferring  life-lines  to 
the  crews  of  wrecked  vessels,  and  may  be  applied  to  the 
movement  of  floating  torpedoes. 

Rockets  are  fired  from  inclined  troughs  or  tubes. 

The  12  pounder  rockets  of  the  following  named  varieties, 


XVI. — PROJECTILES.  47 


fired  at  an  angle  of  elevation  of  8°  15',  gave  the  following 
mean  ranges  and  mean  lateral  errors  (for  the  definition  of 

these  terms  see  Chapter  XXX,  page  24) : 

Range.  Mean  lat.  error. 

Hale  rocket 1312  yards.  37  yards. 

McDonald-Hale  rocket...  2012  .  "  " 


XVII. — FABRICATION    OF    ARTILLERY    PROJECTILES. 


CHAPTER  XVII. 

FABRICATION   OF   ARTILLERY   PRO- 
JECTILES. 

The  fabrication  of  projectiles  involves  reference  to  the 
principles  of  founding,  some  knowledge  of  which  is  neces- 
sary to  a  practical  education. 

Founding,  or  as  it  is  less  properly  called,  castmg,  may  be 
divided  into  three  parts,  viz.: 

I.  Molding :  by  which  a  cavity,  or  ??wldj  is  formed  to  re- 
ceive the  molten  metal;  II.   Melting;  III.  Pouring. 

I.    MOLDING. 
Material  of  Mold. 

Metallic. 

When  the  metal  to  be  cast  is  fusible  at  a  low  temperature, 
so  that  it  will  remain  liquid  for  some  time  after  contact  with 
a  metallic  surface,  the  mold  may  be  made  of  a  less  fusible 
metal.  This  permits  great  exactness  in  the  resulting  casting, 
particularly  if  the  metal  does  not  contract  much  in  cooling, 
and  it  allows  the  mold  to  be  repeatedly  employed."  For 
such  reasons  the  molds  formerly  used  for  making  bullets, 
and  those  now  employed  for  making  fuze-cases  of  pewter, 
and  for  printing-type,  are  metallic. 

Metallic  molds  are  also  used  in  casting  ingots  that  are  to 
be  forged,  and  for  chill  castings,  as  explained  in  the  Chem- 
istry and  hereafter. 

Non-metallic, 

But  when  the  metal  to  be  cast  cools  so  quickly  on  contact 
with  a  metallic  mold  that  it  is  apt  to  set  up  considerable 


2         XVIT. — FABRICATION    OF    ARTILLERY    PROJECTILES. 

internal  strain;  when  it  is  apt  to  form  blow-holes;  and  par- 
ticularly, when  its  temperature  is  so  high  as  to  be  destruc- 
tive to  the  mold,  this  must  be  made  of  sand. 

Because  of  its  refractoriness,  the  sand  used  is  generally 
silicious;  and  to  increase  its  porosity  to  the  gases,  and  its 
cohesiveness,  that  which  is  angular  and  of  moderate  size  is 
preferred.  Sand  also  yields  slightly  to  the  change  in  form 
of  a  casting  while  cooling.  For  example,  a  dumb-bell,  cast 
in  an  iron  mold  would  probably  pull  in  two,  from  longitud- 
inal strain. 

Sand  possessing  all  the  properties  to  be  desired  for 
molding  is  seldom  found  in  a  natural  state.  Accordingly, 
artificial  molding  co77ipositions  are  made  by  mixing  sand 
with  various  proportions  of  clay  or  flour  to  increase  its  co- 
hesiveness; or  with  some  combustible  material  such  as  coal 
dust,  horse  manure  or  straw,  to  increase  its  porosity  at  a 
high  temperature. 

The  addition  of  water  is  necessary  to  give  plasticity;  but 
as  this  causes  blcw-holes,  and  even  dangerous  explosions  to 
occur,  as  little  of  it  as  possible  is  employed.  In  some  cases 
it  is  removed  h^j  drying  the  mold;  or,  when  great  strength 
is  required^  by  baking  it. 

Molding  Compositions. 

The  presence  of  water  or  of  a  combustible  material  in  the 
molding  composition  exercises  an  important  effect  upon  the 
casting.  In  both  cases  the  gases  resulting  from  contact 
with  the  molten  metal  act,  as  in  the  familiar  example  of 
water  in  the  spheroidal  state,  to  prevent  close  contact 
between  the  fluid  metal  and  the  particles  of  sand.  The 
effect  of  this  contact  woujd  be  to  make  a  rough,  gritty 
surface,  destructive  to  cutting  tools.  The  combustible  may 
be  incorporated  with  the  sand  or  applied  upon  the  surface 
of  the  mold. 


XVn. — FABRICATION    OF    ARTILLERY    PROJECTILES.         3 

^lolding  compositions  are  divided  into  three  classes: — 

1.  Green  Sand,  which  is  wholly  or  nearly  in  its  natural 
condition,  and  slightly  damp.  This  is  principally  used  for 
low  grade  castings,  often  molded  in  the  floor  of  the  foundry 
so  as  to  avoid  the  use  of  flasks. 

2.  Dry  Sand,  which  is  artificially  dried  after  molding. 
This  is  used  for  cylindrical  objects,  cast  vertically,  as  it  per- 
mits a  freer  escape  of  gas  than  does  the  green  sand.  It  is 
also  used  for  castings  of  copper  and  brass  on  account  of 
their  greater  conductivity,  the  object  being  to  prevent  their 
iooling  as  rapidly  as  in  the  moist  green  sand.  For  cohesion, 
a  certam  proportion  of  clay  is  mixed  with  the  fresh  sand  ; 
and  to  compensate  for  the  absence  of  water  and  the  incor- 
porated carbon,  sand  which  is  of  a  fine  grain  is  employed  to 
give  a  smooth  surface  to  the  casting. 

3.  Loam.  This  consists  of  a  plastic  mixture  of  clay 
and  sand,  to  which  straw,  etc.,  are  added  for  porosity.  It 
is  used  for  forming  large  volumes  of  revolution  by  the 
operation  of  sweep  moldings  to  be  described.  Such  objects 
are  cast  in  pits,  and  hence  the  old  sand  resulting  is  called 
pit  sand. 

Besides  these  there  are  ^v[\^^\o'^Q^^  parting  sand  2^x\A  facings. 
The  former  is  lighter  in  color  and  of  a  finer  grain  than  that 
employed  in  molding,  and  particularly  free  from  moisture. 
Facings  are  generally  composed  of  carbonaceous  material, 
such  as  black  wash,  a  mixture  of  finely  ground  coal  and  water, 
or  of  dry  flour,  soot,  etc. ;  though  chalk  is  sometimes  em- 
ployed on  account  of  the  CO^  it  gives  out  when  heated. 
Patterns. 

These  are  of  two  classes,  according  as  they  have  a  solid 
or  a  hollow  form.  The  former  may  be  called  positive,  and 
the  latter  negative  patterns.  As  each  kind  of  pattern  is 
intended  to  produce  its  like  in  metal,  the  positive  pattern  is 


4         XVII. — FABRICATION    OF    ARTILLERY    PROJECTILES. 

used  to  form  a  negative  mold,  and  the  negative  pattern,  or 
core  box^  to  form  a  positive  mold  or  core.^ 

To  indicate  in  the  mold  the  position  which  is  to  be  occupied 
by  the  core,  core  prints  are  made  on  the  surface  of  the  pattern. 
These  form  cavities  in  the  sand  into  which  fit  corresponding 
projections  on  the  core. 

Positive  patterns  require  to  be  made  somewhat  larger  than 
the  casting;  the  difference  being  determined  by  the  shrinkage 
of  the  metal  in  cooling  from  the  temperature  of  solidification 
to  that  of  the  atmosphere. 

To  facilitate  their  withdrawal  from  the  sand,  patterns  are 
given  a  smooth  taper  surface;  the  difference  in  diameter  is 
called  the  draught.    This  requirement  influences  the  number 
oi  parts  in  which  a  pattern  shall  be  made. 
Parting  Plane. 

The  parting  plane  is  that  in  which  the  main  sections  or 
parts  of  the  mold  unite.  The  number  of  parts  depends  on 
the  choice  of  the  parting  plane.  Thus,  for  a  rod  of  elliptical 
section,  figure  7,  if  the  parting  plane  contains  either  of  the 
principal  axes,  AB,  CD,  there  will  be  but  two  parts.  But  if 
the  parting  plane  contains  an  oblique  axis,  as  EF,  either  the 
mold  or  the  pattern  must  be  further  subdivided. 

The  parting  plane  is  accordingly  taken  so  as  to  include 
either  the  maximum  or  the  minimum  diameter  of  the  pattern. 
Long  cylindrical  pieces  are  therefore  parted  on  an  axial 
plane,  as  this  direction  gives  them  abundant  draught. 

The  parting  plane  is  the  plane  of  reference  for  most  of 
the  operations  of  molding. 

Negative  patterns  part  on  an  axial  plane  to  facilitate  the 
withdrawal  of  the  core,  which  is  often  made  truly  cylindrical, 
or  of  a  form  not  readily  admitting  ef  its  withdrawal  in  the 
direction  of  the  axis. 


*  This  distinction  is  introduced  only  for  purposes  of  instruction;  th« 
©rdinary  clfissifigation  being  simply,  patterns  and  corgi. 


XVII. — FABRICATION    OF    ARTILLERY    PROJECTILES. 


Material. 

The  material  of  which  a  pattern  is  made  depends  upon 
the  number  of  times  which  it  may  be  employed,  and  some- 
what upon  its  size.  If  made  of  wood,  it  should  be  built  up 
of  pieces  having  the  grain  running  in  different  directions  so 
as  to  prevent  its  warping. 

In  some  cases  where  large  castings  are  made  by  sweep 
moldings  the  expense  of  patterns  may  be  spared,  and  the 
necessary  concave  and  convex  surfaces  of  revolution  formed, 
by  templets  revolving  about  an  axial  spindle.  The  differ- 
ence of  radii  between  the  core  and  the  mold  so  formed 
determines  the  thickness  of  the  casting. 
Flask. 

The  sand  forming  the  mold  is  supported  by  an  outer  frame 
or  box,  called  the  flask.  As  many  separate  flasks  are  used 
as  there  2iX&  parts  in  the  mold. 

For  ordinary  molding  a  two-part  flask  suffices;  the  part 
uppermost  in  casting  being  called  the  cope,  and  the  lower 
part  the  drag. 

Lateral  motion  between  the  parts  of  the  flask  is  prevented 
by  dowels,  and  the  cope  is  prevented  from  rising  under  the 
hydrostatic  pressure  of  the  melted  metal  by  weights  or 
clamps,  or  flanges  bolted  or  keyed  to  the  sides  of  the  drag. 

The  flask  should  conform  to  the  general  shape  of  the 
casting  so  as  to  avoid  great  differences  in  the  rate  of  cool- 
ing and  to  facilitate  the  operations  of  molding.  It  often 
contains  cross  pieces  to  support  the  sand. 

For  loam  castings,  the  flask  may  consist  of  a  pit,  sunk 
beneath  the  surface  of  the  foundry  floor. 

Together  with  the  flask  is  used^  as  a  temporary  bottom, 
the  folloiu  board.  This  may  have  a  plane  surface  next  the 
flask,  or  may  contain  in  relief  one  or  more  patterns  so  placed 
as  to  determine  the  proper  position  of  the  corresponding 
molds. 


6         XVII. — FABRICATION    OF    ARTILLERY    PROJECTILES. 

Molding  Tools. 

These  consist  of  shovels,  watering  pots  and  sieves  for 
mixing  the  sand;  rammers  for  packing  it  around  the  pattern: 
trowels  of  various  forms  for  repairing  imperfections,  porous 
bags  containing  parting  sand  and  facings,  and  venting  wires 
with  which  to  open  an  escape  for  the  occluded  gases. 

„      ,  II.  MELTING. 

Metal. 

The  properties  of  the  metal  employed  depend  on  the  size 
of  the  casting  and  the  nature  of  the  projectile. 

A  decided  advantage  in  tenacity  follows  the  use  of  a  large 
proportion  of  gun-steel  scrap. 

The  higher  the  grade  of  iron,  the  stronger  it  is;  but  the 
less  fluid  it  is  when  melted,  and  the  greater  is  the  shrinkage 
and  the  difficulty  of  subsequently  reducing  it  to  finished 
size.  The  effects  of  shrinkage  are  relatively  greatest  in 
small  molds. 

Consequently  for  field  projectiles  grey  iron  is  used,  and 
for  those  of  larger  size  that  which  is  more  mottled  or  con- 
tains a  larger  proportion  of  white  iron.  For  chilled  shot  a 
mixture  is  made  of  charcoal  and  anthracite  pig  irons,  or  of 
old  shot  and  car  wheels  in  about  equal  proportions.  The 
components  first  named  in  each  pair  give  toughness,  and  the 
latter  the  desired  hardness  to  the  casting.  Car  wheels  are 
cast  in  chills  surrounding  the  tread,  while  the  centers  are 
cast  in  sand.  The  chill  gives  hardness  where  abrasion  is  to 
be  feared,  and  the  sand  causes  the  interior  to  cool  more 
slowly,  thus  converting  it  into  grey  iron  and  giving  it  the 
softness  and  toughness  required.  The  same  principle  is 
applied  in  the  chill  casting  shown  in  figure  6. 

Furnaces. 

The  cupola,  or  the  reverberatory  furnace  is  employed 
according  to  the  quantity  and  quality  of  the  projectiles;-  to 
be  cast. 


XVII. — FABRICATION    OF    ARTILLERY    PROJECTILES.         ? 

III.  POURING. 

To  diminish  the  shrinkage  the  iron  is  poured  at  the  lowest 
temperature  consistent  with  fluidity;  and  to  make  the  shrink- 
age uniform,  small  ladles  filled  from  the  furnace  are  pre- 
ferred to  the  large  ladles  used  for  great  castings. 

The  melted  metal  is  skimmed  while  pouring. 

FABRICATION  OF  PROJECTILES. 

To  apply  the  preceding  principles  we  will   explain  the 
manufacture  of  the  4.5  inch  shot  and  shell  of  the  Butler 
pattern,  referring  to  figures  1  to  6. 
Patterns, 

The  parting  plane  is  taken  at  the  junction  of  the  body  of 
the  projectile  and  the  tenon  for  the  rotating  ring;  concen- 
tricity of  these  parts  being  secured  by  an  axial  dowel. 

The  diameter  of  the  cylindrical  portion  is  enlarged  rela- 
tively to  the  maximum  diameter  of  the  head;  so  that,  during 
the  reduction  of  the  body  to  its  finished  size,  the  curvature 
of  the  head  near  the  front  bearing  shall  not  be  distorted. 

For  the  shot  a  teat  provides  a  small  surplus  of  metal  near 
the  point  and  ensures  a  full  casting  there.  The  teat  is  after- 
wards turned  off  to  the  curvature  shown  in  the  dotted  lines. 

The  shell  pattern  has  a  projecting  spindle  as  a  core  print. 
This  terminates  at  «  in  a  conical  surface,  so  that  in  spite  of 
wear  and  unavoidable  variations  in  manufacture  it  may  be 
accurately  centered  in  the  cross  piece,/,  of  the  flask.  Such 
conical  bearings  are  frequently  used  in  construction. 

As  it  is  difficult  for  the  sand  to  penetrate  the  small  annular 
cavity  above  the  main  portion  of  the  core,  this  is  separately 
formed  in  the  mold  box ^  figure  4,  before  the  spindle  is  seated 
in  the  core  box.  The  mold  box  represented  is  of  wood, 
constructed  on  the  same  plan  as  the  core  box. 

For  a  double-walled  shell  the  core  is  covered  with  a  cast 
iron  corrugated  sleeve  of  the  form  desired.    The  resistance 


8         XVn. — FABRICATION   OF    ARTILLERY    PROJECTILES. 

which  this  offers  to  the  contraction  of  the  metal  about  it, 
explains  why  this  ingenious  form  of  projectile  is  not  more 
largely  employed. 

The  patterns  for  the  gate^  by  which  the  melted  metal  is 
admitted  to  the  mold,  and  the  riser,  by  which  the  air  and 
scoriae  escape,  are  plain  conical  sticks,  sometimes,  as  in  figure 
6,  made  in  two  parts  to  facilitate  their  removal. 

Core  Box. 

This  is  of  iron,  made  in  halves  uniting  on  an  axial  plane. 
It  is  bored  out  when  bolted  together  through  the  four  holes 
shown,  and  brought  into  correct  opposition  by  the  four 
conical  dowels  near  the  holes. 

To  form  the  core,  an  iron  tube,  called  the  spindle,  per- 
forated with  many  holes  and  provided  with  a  conical  bear- 
ing as  at  a,  (all  figures,)  is  wrapped  with  tow  and  secured  in 
the  core  box  by  a  nut,  n.  Sand  is  then  rammed  around  the 
spindle,  the  final  form  of  the  core  being  given  by  the  cup,  ^, 
so  shaped  as  to  strengthen  the  base  of  the  shell. 

Flask. 

For  large  projectiles  this  is  cylindrical;  but  for  small  ones 
it  may  be  of  rectangular  cross  section  so  as  to  contain  several 
molds.  For  molding  shell  or  cored  shot,  a  cross  piece,  /, 
figures  5  and  6,  containing  a  conical  cavity,  is  so  fixed  in  the 
flask  that  the  parting  plane  of  the  pattern  shall  fall  in  the 
parting  plane  of  the  flask.  For  some  projectiles,  admitting 
of  complete  perforation,  two  cross  pieces  are  provided.  In 
such  cases  the  conical  bearings  are  not  required. 

To  give  greater  strength  to  the  flask  and  to  preserve  the 
concentricity  of  the  projectile  the  parting  plane  is  one  of 
right  section. 

Position  of  the  Pattern  in  the  Flask. 

Shot  are  cast  point  down,  so  as  to  give  density  to  the 
point- 


XVII. FABFICATION    OF    ARTILLERY   PROJECTILES. 


Casting  shell  point  down  leads  to  porosity  and  weakness 
of  the  base  which  may  cause  them  to  fail  in  the  gun.  But 
when  a  front  fuze  is  used,  as  in  figure  5,  if  the  shell  were 
cast  point  up,  the  feeding  of  hot  metal  from  the  riser  against 
the  thinly  protected  spindle  would  soften  it  and  cause  it  to 
bend.  This  objection  does  not  apply  when  the  fuze  is  in  the 
bottom  of  the  shell. 

On  account  of  the  difficulty  of  handling  heavy  chills^ 
chilled  shot  are  always  cast  point  down.  To  prevent  the 
wear  of  the  chill  from  the  hot  metal,  which  limits  its  life  to 
about  50  casts,  removable  linings  are  employed.  Following 
the  general  principle  which  requires  a  symmetrical  arrange- 
ment of  the  parts  of  the  mold,  and  to  prevent  its  cracking 
from  unequal  expansion,  the  exterior  of  the  chill  should 
follow  the  profile  of  the  mold. 

Gate  and  Eiser. 

For  large  projectiles,  figure  6,  the  gate  enters  the  mold 
preferably  from  below,  so  as  to  avoid  splashing,  and  tangen- 
tially,  to  give  a  rotary  motion  to  the  ascending  column  of 
metal,  and  so  sweep  the  scoriae  away  from  its  axis. 

The  riser  is  intended: — 

1st.  To  allow  free  vent  to  the  included  air  and  gases. 
These  are  sometimes  lighted  to  assist  their  dispersion. 

2nd.  To  allow  the  melted  metal  to  be  stirred  during  the 
solidification.  This  liberates  the  gases  and  scoriae;  and, 
since  fused  metals  are  poor  conductors,  it  facilitates  simul- 
taneous solidification,  and  thus  diminishes  internal  strain. 

3rd.  To  feed  the  hot  metal  into,  and  sometimes  to  make 
it  flow  through  the  mold. 

By  careful  stirring  and  feeding,  shot  as  large  as  12-inch 
have  recently  been  cast  solid. 

Small  projectiles  may  be  cast  in  groups  with  one  gate  for 


10      XVII. — FABRICATION    OF    ARTILLERY    PROJECTILES. 

several  molds;  but  each  mold  should  have  an  independent 
riser. 

Large  spherical  projectiles  are  sometimes  cast  in  strings^ 
connected  by  necks  which   increase  in  diameter  upward. 

OPERATION    OF    MOLDING. 

Secure  the  spindle  of  the  shell  pattern  in  its  seat  in  the 
cross  piece  by  the  nut  n.  Invert  the  drag  so  that  the  shell 
shall  rest  upon  the  follow  board  on  the  parting  plane.  Place 
the  main  shot  pattern  upon  the  point  of  the  follow  board 
indicated  by  a  dowel.  Dust  the  follow  board  and  the  pat- 
terns with  parting  sand.  Fill  the  mold,  ramming  it  suffi- 
ciently to  make  it  solid,  but  not  so  much  so  as  to  unduly 
diminish  its  porosity  ;  this  requires  much  experience. 

Invert  the  drag,  holding  it  between  the  follow  board  and 
another  board. 

Remove  the  follow  board;  place  the  base  patterns  on  the 
corresponding  bodies  and  secure  the  cope  by  the  dowels  to 
the  drag.  Dust  as  before,  and  fill  the  mold;  inserting  the 
patterns  for  the  gate  and  riser  at  the  proper  time. 

Place  the  follow  board  on  the  cope;  lift  off  the  cope  and 
reverse  it;  remove  the  patterns  which  it  contains:  they  may 
require  to  be  slightly  jarred,  so  as  to  loosen  them  in  the 
sand.     Do  the  same  for  the  patterns  in  the  drag. 

After  repairing,  drying,  and  facing  the  mold  with  black 
wash  or  its  equivalent,  place  and  secure  the  core  which  has 
been  similarly  treated. 

Replace  the  cope  and  secure  it  to  the  drag  by  such  means 
as  shown  in  figure  6.     The  mold  is  then  ready  for  pouring. 

FINISHING. 

Preliminary  Operations. 

As  soon  as  the  metal  has  become  sufficiently  solid,  and 
while  still  hot,  and  therefore  weak,  the  flask  is  opened 
and  the  excrescences  left  by  the  gate  and  riser  broken 


XVII. — FABRICATION    OF    ARTILLERY    PROJECTILES.       11 

off.  To  facilitate  contraction  about  the  core  the  spindle  is 
withdrawn.  This  may  be  easily  done,  since  the  tow  with 
which  it  was  surrounded  has  been  consumed.  To  retard 
the  cooling  of  the  casting  it  is  then  covered  with  the 
loose  sand  which  formed  the  mold.  When  cool,  the  cavity 
is  carefully  cleaned  from  sand. 

The  proper  cylindrical  form  is  given  by  the  lathe,  the 
most  important  of  all  machine  tools. 
Description  of  the  Lathe. 

A  lathe  is  intended  to  form  surfaces  of  revolution  by 
causing  an  object  to  revolve  on  one  of  its  axes  while  it 
is  acted  on  by  a  cutting  tool  to  which  motion  either  along 
the  axis  of  revolution,  at  right  angles  to  it,  or  in  both  compo- 
nent directions  may  be  given,  either  automatically  or 
by   hand. 

Figure  8  shows  a  lathe,  in  which  A  is  the  frame,  the 
upper  surface  of  which  is  formed  in  parallel  rectilinear 
ways  or  guides.  M,  is  the  fixed  head  stock,  in  which 
revolves  the  cone  pulley  P.  This  may  be  made  to  carry 
with  it  the  concentric  live  spuidlCy  S,  and  the  face-plate, 
F,  or  may  revolve  independently  of  these  parts.  The 
spindle  is  hollow  and  carries  on  its  interior  the  conical 
center,  C.     Its  exterior  is  threaded  for  the  face-plate. 

T,  is  the  movable  tail  stock;  it  contains  the  dead  spindle, 
S,  provided  with  a  conical  center  like  that  in  the  live 
spindle.  The  tail  stock  may  be  clamped  on  the  ways  at 
any  desired  distance  from  Fj  a  close  adjustment  of  S 
may  be  made  by  the  screw  Z>,  which  is  clamped  by  the 
set  screw  E. 

The  slide  rest  G,  the  invention  of  the  great  English 
mechanician.  General  Samuel  Bentham,  has  been  used  for 
only  about  a  century.  To  its  invention  is  attributed  the 
practical  success  of  the  steam  engine;  it  having  been  pre- 
viously   found    impossible    to    produce    truly    cylindrical 


12       XVII. FABRICATION    OF    ARTILLERY    PROJECTILES. 

surfaces  of  large  diameter.  The  slide  rest,  carrying  the 
cutting  tool,  derives  its  motion  from  the  rotation  of  the 
live  spindle  by  means  of  a  change  gear,  H,  which  connects 
the  outer  end  of  the  live  spindle  with  the  feed  screw,  J. 
The  feed  screw  passes  through  a  nut  on  the  lower  side 
of  the  slide  rest,  with  which  it  may  be  thrown  into  and 
out  of  gear. 

Variations  in  Speed. 

The  necessary  cutting  speed,  or  the  velocity  of  the  surface 
in  contact  with  the  tool,  varies  with  the  nature  and  diameter  of 
the  material  to  be  turned.  The  angular  velocity  of  the  work 
may  accordingly  be  varied  by  means  of  the  steps  on  the 
cone  pulley.  A  similar  pulley  above  the  lathe,  with  its 
axis  reversed,  receives  the  power  from  the  main  line  of 
shafting  by  the  driving  belt,  d,  and  transmits  it  to  the  lathe 
by  means  of  the  working  belt,  w.  The  upper  pulley  is 
mounted  on  an  axis  provided  with  a  fast  and  a  loose 
pulley,  /  and  /,  so  that  the  lathe  may  be  set  in  motion 
or  stopped  by  varying  the  position  of  the  driving  belt. 
This  arrangement,  which  is  indispensable  to  all  machine 
tools,  is  called  a  counter-shaft.     See  figure  9. 

Where  great  power,  and  therefore  slow  speed  Is  re- 
quired, the  back  gear,  figure  10,  is  employed.  This  consists 
of  two  pinions,  a  and  b,  mounted  on  an  axis,  c,  parallel 
to  that  of  the  spindle  $,  and  so  placed  that  when  a  engages 
with  a  toothed  wheel,  d,  which  is  secured  to  the  spindle, 
b,  shall  engage  with  one  of  corresponding  size,  g,  upon 
the  cone  pulley. 

To  use  this,  the  cone  pulley  is  detached  from  d,  and 
revolves  freely  upon  the  spindle.  The  back  gear  may 
then  be  engaged  with  g  and  d.  The  ratio  of  the  diameters 
of  ^,  b,  a,  d,  indicates  the  resulting  gain  in  power. 

By  varying  the  change  gear  any  desired  ratio  can  be 
obtained  between  the  angular  velocity  of  the  work  and  that 


Xvit. — ^Fabrication  Of  artillery  projectiles.     13 

of  the  translation  of  the  tool.    In  this  way  screws  of  any 
desired  pitch  may  be  cut. 
Support  of  Work. 

The  work  may  be  supported  by  the  conical  centers  form- 
ing the  adjacent  ends  of  the  live  and  dead  spindles.  For 
this  purpose  it  is  provided  with  corresponding  depressions, 
which  are  called  center  niarks^  at  the  ends  of  the  axis 
of  revolution.  As  a  rule  these  center  marks  are  left  in 
finished  work,  as  they  permit  pieces  containing  them  to  be 
reworked  or  repaired.  The  work,  in  turning  between 
centers,  is  caused  to  rotate  by  means  of  a  dog^  figure  11; 
the  tail  of  the  dog  fits  in  a  radial  notch  in  the  face  plate. 

In  certain  cases  when  turning  between  centers  is  impracti- 
cable, one  end  of  the  work  is  secured  to  the  face  plate 
by  means  of  the  chuck.  This  is  provided  with  three  radial 
set  screws  capable  of  simultaneous  operation.    See  figure  12. 

In  such  cases,  and  to  prevent  the  springing  of  long  pieces 
in  turning  betv/een  centers,  an  intermediate  back  rest^  By 
figure  8,  is  sometimes  employed. 
Uses  of  the  Lathe. 

It  is  evident  that  the  lathe  may  be  used  for  boring  as 
well  as  for  turning  external  surfaces,  and  that  by  the  use 
of  a  hook-shaped  tool,  passed  through  the  fuze  hole, 
such  cavities  as  that  of  the  shell  can  be  turned. 

Also,  that  plane  surfaces  can  be  formed  by  omitting  the 
longitudinal  translation  of  the  tool,  or  that,  preserving  this 
motion  and  guiding  the  tool  by  means  of  a  template, 
any  desired  surface  of  revolution  may  be  exactly  repro- 
duced. 

By  replacing  the  center  in  the  live  spindle  by  a  suitable 
tool,  against  which  the  work  may  be  pressed  by  the  back 
spindle,  also  without  its  center,  the  work  may  be  drilled. 

If  the  tool  be  made  after  the  manner  of  a  very  thick 
circular  saw,  the  edge  of  which  may  be  either  cylindrical 


14      XVII. — FABRICATION    OF    ARTILLERY   PROJECTILES. 

or  form  almost  any  surface  of  revolution,  the  work  may 
be  moved  along  a  plane  director  at  right  angles  to  the 
plane  of  rotation,  so  as  to  form  a  new  surface  composed 
of  parallel  rectilinear  elements,  and  having  its  cross  section 
correspond  to  the  contour  of  the  tool.  This  operation 
is  called  milling;  it  is  of  the  greatest  importance  in  the 
manufacture  of  fire  arms,  sewing  machines  and  others  in 
which  the  interchangeability  of  the  parts  is  required.  To 
the  general  use  of  milling  machines  may  be  largely  attri- 
buted the  eminence  of  certain  American  manufactures. 

The  principal  advantages  of  machines  eniploying  the 
principles  of  the  lathe  depend  upon  the  continuity  of 
the  motion  and  the  ease  with  which  it  may  be  varied. 

Final  Operations. 

Projectiles  of  soft  iron  are  finished  externally  on  the 
lathe,  or  may  be  forced  by  an  hydrostatic  press  through 
a  circular  steel  die.  The  former  method  is  preferred.  The 
head  is  not  touched,  in  order  that  the  skin^  which  is  the 
hardest  part,  may  remain  intact. 

Chilled  shot  require  special  treatment  by  a  grindstone 
or  a  peculiarly  shaped  prismatic  tool,  figure  13.  This 
forms  a  scraping,  instead  of  the  paring  edge  generally 
employed;  it  is  less  apt  to  spring  away  from  the  work 
on  meeting  any  portions  which  are  excessively  hard,  and 
may  be  easily  and  accurately  sharpened  by  a  cylindrical 
grindstone. 

The  natural  silicious  sandstone  is  frequently  replaced 
by  an  artificial  stone  composed  of  emery  concreted  by  a 
cement. 

FABRICATION  OF  STEEL  PROJECTILES. 

Those  are  intended  for  piercing  armor.  Either  cored 
shot  or  shell  are  employed.     They  may  be  either  cast  or 


3tvn. — Fabrication  op  ARtiLLERY  projectiles.    15 

forged,     The  former  are  the  cheaper;  the  latter,  so  far,  the 

stronger. 

Steel  Cast  Projectiles. 

A  rather  silicious  metal  is  preferred.  In  order  to  fix  the 
carbon,  both  head  and  body  are  cast  in  a  chill  mold;  this  is 
surmounted  by  a  sand  mold  containing  the  sinking  head. 
After  cutting  off  the  sinking  head,  the  projectile  is  hardened, 
the  point  being  heated  most.  It  is  cooled  by  first  dipping 
the  point  in  water  and  then  immersing  the  whole  projectile 
in  oil.  In  order  to  further  soften  the  base  so  as  to  permit 
the  screw  thread  in  the  fuze  hole  to  be  cut,  the  base  is  an- 
nealed while  the  point  is  kept  in  running  water.  To  avoid 
this  operation,  the  base  of  the  projectile  may  contain  a  piece 
of  wrought  iron  pipe,  around  which  it  has  been  cast,  as  in 
chilled  shot. 
Forged  Steel  Projectiles. 

These  are  hammered  into  shape  from  bars  of  suitable  size, 
turned  inside  and  out,  and  hardened  and  tempered  as  above 
described. 

Steel  shrapnel  are  now  (1891)  economically  made  by  elec- 
tro-welding.    Chapter  XV,  page  23. 

ROTATING  BANDS. 

Copper  is  preferred  on  account  of  its  softness  and  strength 
and  its  resistance  to  erosion  by  the  gases.  Its  uniformity  is 
increased  by  adding  about  5  per  cent  of  zinc.  This  forms 
an  alloy  known  2,%  gilding  metaiy  used  in  the  manufacture 
of  cartridges,  cheap  jewelry  and  the  bell  buttons  used  in 
the  Cadet  uniform. 

The  bands  are  applied  in  two  general  ways. 

I.  In  Casting. 

1.  The  band  may  be  cast  in  place  on  the  projectile.  This  is 
the  simplest  plan,  but  does  not  always  make  a  good  casting. 

2.  An  annular  band,  the  cross  section  of  which  is  as  shown 


16      XVII, — FABRICATION    OF    ARTILLERY    PROJECTILES. 

in  figure  14,  is  placed  in  the  bottom  of  the  mold  before  the 
metal  composing  the  body  of  the  projectile  is  poured.  To 
keep  it  from  melting,  it  may  be  surrounded  by  a  much  thicker 
band  of  the  same  material,  or  by  a  hollow  band  through 
which  runs  a  stream  of  water. 

II.  After  Casting. 

A  seat  for  the  band  of  the  undercut  section  shown  in 
figure  15,  is  turned  in  the  body  of  the  projectile  and  the  band 
forced  into  this  groove  by  hand  or  by  machine. 
.  1.  By  hand. 

In  this  case  the  band  may  be  either  a  straight  rolled  strip 
with  bevelled  ends,  as  seen  in  figure  16;  or  for  large  pro- 
jectiles it  may  be  cast  in  the  form  of  a  semi-circular  hoop. 
In  both  cases  the  placing  of  the  band  is  done  gradually  by 
the  hammer. 

2.  By  machine. 

The  band  complete  is  slipped  over  the  projectile  until 
opposite  its  seat;  it  is  then  set  in  by  powerful  presses  acting 
radially. 

INSPECTION  AND  PROOF  OF  PROJECTILES. 
Comparison. 

It  can  hardly  be  too  strongly  insisted  upon  that  the  in- 
spection, not  only  of  projectiles;  but  of  powder  and  of  arms 
of  all  kinds  is  only  preparatory  for  and  subordinate  to,  the 
proof.  The  inspection  may  detect  the  causes  of  failure  in 
proof,  and  often  applies  to  many  more  articles  than  can  be 
profitably  proved;  but  that  it  can  not  wholly  replace  it,  is 
proverbially  and  actually  true. 

INSPECTION, 

Object  of  the  Inspection. 

The  object  of  the  inspection  is  to  detect  defects  of  work- 
manship and  material  which  may  affect  the  successful  oper- 
ation of  the  projectiles. 


XVII. — FABRICATION    OF    ARTILLERY    PROJECTILES.       17 

As  it  is  impossible  to  make  all  projectiles  of  exact  dimen- 
sions, certain  variations  are  allowed  in  manufacture.  For 
sake  of  economy,  the  greatest  variation  or  tolerance^  con- 
sistent with  safety  and  efficiency,  should  be  allowed;  both  in 
workmanship,  as  shown  by  the  gauges,  and  in  the  material. 
This  remark  is  general. 
Instruments. 

Maximum  and  minimum  ring  gauges,  see  Chapter  IV,  page 
11;  a  hollow  cylinder  gauge,  five  calibers  long;  a  profile 
gauge;  a  rolling  table,  and  calipers  for  measuring  the 
thickness  of  the  metal  at  the  sides  and  bottom  of  the  cavity 
are  the  principal  instruments  required.  Besides  these  there 
are  various  gauges  to  verify  the  dimensions  of  the  fuze 
hole,  and  of  the  rotating  device  and  its  seat.  Also  various 
tools  for  exploring  suspicious  cavities  or  defects. 

An  easy  method  of  detecting  small  differences  in  the 
diameter  of  cylindrical  holes  consists  in  the  use  of  a 
slightly  conical  bar  of  steel,  the  diameter  of  different 
sections  of  which  is  marked  upon  its  length  after  the 
manner  of  a  diagonal  scale  of  equal  parts. 

Except  for  the  rolling  table,  the  names  of  these  instru- 
ments and  their  appearance  as  represented,  figure  17, 
sufficiently  indicate  their  employment. 

The  rolling  table  is  of  iron  with  two  parallel  ribs  at  a 
distance  apart  slightly  less  than  the  length  of  the  cylindrr- 
cal  portion  of  the  projectile.  These  ribs  are  brought  truly 
level,  so  that  a  concentric  projectile  will  assume  a  position 
of  equilibrium  of  indifference. 
Process. 

The  presence  of  fissures  in  hollow  projectiles  may  be 
detected  by  exposing  them  to  an  internal  jet  of  steam,  or  by 
observing  whether  after  plunging  them  in  water,  notable 
differences  in  the  rate  of  drying  occur. 

When  it  is  possible,  the  quality  of  the  material  is  tested 


18      XVII. — FABRICATION    OF    ARTILLERY    PROJECTILES. 

by  a  specimen  cut  from  the  body  of  a  projectile.  For 
chilled  shot  this  is  not  possible;  so  that  a  cast  specimen 
may  be  tested  and  compared  with  those  mixtures  which 
have  given  good  results.  A  certain  proportion  of  such 
projectiles  are  also  split  so  as  to  expose  the  chill.  The 
homogeneity  of  such  shot  is  also  tested  by  striking  them 
with  a  hammer  at  the  junction  of  the  body  and  head:  a 
clear  sound  should  be  produced.  In  spite  of  the  inspec- 
tion, such  projectiles  are  liable  to  split  spontaneously  from 
internal  strain. 

In  order  to  stimulate  the  contractor  to  greater  care, 
projectiles  are  inspected  in  lots^  the  failure  of  a  certain 
proportion  of  which  for  defects  of  material  suffices  to 
condemn  the  entire  lot.  This  is  then  permanently  marked 
so  as  to  prevent  its  being  again  presented  for  inspection. 

This  rule  is  applied  also  to  defects  in  workmanship  when 
the  number  of  objects  is  too  great  to  permit  of  the  inspec- 
tion of  every  one,  as  in  the  ammunition  for  small  arms. 

PROOF   OF    PROJECTILES. 

Careful  inspection  generally  suffices  for  all  but  those  in- 
tended for  use  against  armor.  But  in  all  cases  it  is  more 
conclusive  to  supplement  this  by  a  proof,  as  by  firing  for 
accuracy. 

Armor  piercing  projectiles  are  proved  by  firing  about  one 
per  cent  of  a  lot  against  wrought  iron  armor  about  one 
caliber  thick ;  the  chilled  iron  striking  normally  and  the  steel 
at  about  20  degrees  to  the  normal.  Upon  the  performance 
and  endurance  of  the  proof  projectiles,  fired  with  penetrating 
charges,  depends  the  acceptance  of  the  lot. 


XVIII. — MEANS   OF   COMMUNICATING    FIRE. 


CHAPTER   XVIII. 

MEANS  OF  COMMUNICATING  FIRE. 

These  may  be  divided  into  two  classes,  viz.; 

1.  Those  intended  for  igniting  stationary  charges  in  guns 
and  mines.  It  includes  various  forms  of  matches  and 
primers. 

2.  Fuzes,  which  are  intended  to  be  used  in  moving  objects, 
such  as  explosive  projectiles,  torpedoes,  etc. 

CLASS    I. 

MATCHES  AND   PRIMERS. 

According  to  the  time  elapsing  between  their  own  igni- 
tion and  that  of  the  charge,  these  may  be  considered  as 
relatively  slow  or  rapid. 

IGNITERS    COMPARATIVELY    SLOW. 

Slow-Match, 

This  was  formerly  employed  for  igniting  the  port-fire, 
by  which  the  loose  gunpowder  priming  laid  around  the 
upper  orifice  of  the  vent  was  fired.  It  is  now  employed 
only  for  preserving  fire.  If  made  of  hemp  rope,  combustion 
is  retarded  by  saturating  it  with  lead  acetate,  or  the  lye 
of  wood  ashes.  If  of  cotton  it  is  only  necessary  that 
the  strands  be  well  twisted.  Slow  match  burns  from  4 
to  5  inches  per  hour. 

Quick-Match  is  used  to  communicate  fire,  as  in  fire-works 
and  in  experimental  work  of  a  dangerous  character.  It 
is  made  of  candle  wick,  steeped  in  a  mixture  of  mealed 


8  XVm. — MEANS   OF    COMMUNICATING    FIRE. 

powder  and  gummed  spirits,  wound  on  a  reel,   dredged 
with  mealed  powder  and  left  to  dry.     ^t  burns  at  the  rate 
of  about  3  inches  per  second. 
Varieties  of  duick-Match. 

The  rate  of  burning  may  be  much  increased  by  enclos- 
ing the  quick-match  in  a  paper  tube;  see  Chapter  VIII. 

If,  instead  of  paper,  the  envelope  be  made  more  pliable 
and  strong,  as  by  a  spiral  wrapping  of  cloth  around  a 
central  core  of  fine  powder,  the  ordinary  blastings  or  Bick- 
ford  fuze  results.  This  inflames  at  a  less  rapid  rate  than 
the  kind  just  named. 

A  tube  of  lead  or  one  of  its  alloys  may  replace  the 
weaker  envelopes  above  described  and  instead  of  simply 
fitting  it  closely,  the  tube,  enclosing  the  core,  may  be 
drawn  as  one  mass  after  the  manner  of  wire. 

If  gun-cotton  be  used  for  the  core,  a  most  convenient 
and  rapid  form  of  detonator  results. 

IGNITERS    COMPARATIVELY    RAPID. 

Caps  and  Detonators. 

These  consist  of  cups  or  tubes  made  by  means  of  a 
double  punch,  figure  1,  the  inner  member  of  which,  /, 
passes  through  a  conical  hole,  h,  of  somewhat  larger  diam- 
eter in  a  stationary  piece,  d^  called  a  die.  The  outer 
punch,/',  which  is  concentric  with  the  inner  and  fits  closely 
to  it,  as  it  descends  into  a  shallow  cylindrical  depression 
at  the  mouth  of  the  die,  shears  from  a  thin  copper  ribbon  a 
disc  which  it  holds  by  the  edges  while  the  inner  punch  forms 
it  into  a  cup.  The  elasticity  of  the  cup  causes  its  open  end  to 
expand  as  soon  as  it  has  passed  through  the  die :  this  strips 
it  from  the  punch  as  the  latter  rises  for  another  stroke.  The 
cup  is  elongated  into  a  tube  by  the  successive  operation  of  a 
series  of  single  punches  and  dies  of  gradually  decreasing  di- 
ameter,   See  plates  Chapter  XXVII,    This  operation,  which 


XVIIl.— MEANS  OF  COMMUNICATING   FIRE.  3 

resembles  closely  that  of  rollings  in  chapter  XV,  is  of  great 
utility  in  the  arts.  For  military  purposes  it  is  principally 
used  in  the  manufacture  of  metallic  cartridges. 

For  percussion  caps  for  small  arms,  the  tube  receives 
a  charge  of  moist  fulminating  composition.  This  is  pre- 
vented from  falling  out,  when  dry,  by  a  disc  of  tin  foil, 
held  in  by  varnish. 

The   construction   of  the   detonator   has   already  been 
described  in  chapter  XIV. 
Cannon  Primers. 

These  are  of  two  classes,  according  as  they  are  fired 
by  friction  or  electricity. 
I.  Friction  Primers. 

The  friction  primer  presents  the  following  advantages 
over  the  method  of  firing  cannon  described,  page  1.  It 
is  portable,  certain  and  rapid;  it  affords  the  means  of  firing 
pieces  at  a  distance,  and  does  not  attract  the  attention  of 
the  enemy's  marksmen  at  night. 

According  to  the  direction  of  the  vent,  friction  primers 
are  divided  into  two  classes. 

I.  Radial  Vent. 

The  primer  used  in  the  military  service  of  the  United 
States  consists  of  two  copper  tubes,  soldered  at  right  angles 
to  each  other,  figure  2. 

The  short  tube  contains  a  charge  of  friction  composition, 
(Sbg  S3  and  K  CIO3)  inserted  moist  and  surrounding  the 
roughened  end  of  a  wire,  the  outer  extremity  of  which 
forms  a  loop  for  the  lanyard.  The  long  tube  is  filled  with 
fine  powder,  retained  by  a  wad  of  wax.  The  nib  of  the 
wire  is  folded  over  the  end  of  the  short  tube,  so  as  to 
prevent  its  accidental  displacement  and  the  firing  of  the 
composition  in  consequence. 

For  large  guns,  the  column  of  fine  powder  may  surmount 


4  3^\ltt.--MEAMS  OJ*  CoMMttNlCATmc  MVlU. 

a  pellet  of  compressed  powder  which  will  be  shot,  burning, 
into  the  cartridge. 

In  some  services  the  cross  tube  is  omitted  and  the  wire, 
inserted  axially,  is  withdrawn  by  a  motion  which  causes  it  to 
bend  continuously  around  the  edge  of  the  vent.  See 
figure  3. 

2.  Axial  Vent, 

As  the  discharge  serves  to  expel  the  empty  tube  with 
great  velocity,  unless  it  be  thrown  upward  it  may  injure 
the  bystanders.  On  this  account,  and  also  to  prevent  the 
erosion  of  the  vent  by  the  escaping  gas,  an  ohtwating prbner 
is  screwed  into  a  proper  seat  concentric  with  the  vent. 
Figure  4  represents  an  obturating  axial  friction  primer. 
When  the  wire  is  withdrawn,  the  conical  portion,  c,  finds 
a  corresponding  seat  at  the  end  of  the  cavity  surrounding 
the  wire.  This  prevents  the  escape  of  gas  through  the  hole, 
while  the  escape  around  the  primer  is  prevented  by  the 
radial  expansion  of  the  thin  edge  in  which  the  portion 
nearest  to  the  charge  is  formed. 

The  stop,  ^,  prevents  the  primer  from  being  screwed  in 
too  far,  and  the  enlargement,  ^,  serves  a  similar  purpose  for 
the  wire. 
II.  Electric  Primers. 

These  are  used  for  firing  charges  at  a  considerable 
distance,  as  in  certain  cases  in  modern  warfare  when  the 
gun  is  so  protected  that  the  object  is  invisible  from  its 
neighborhood;  so  that  the  pointing  and  firing  are  controlled 
by  a  distant  observer.  By  this  means  also,  the  simultaneous 
discharge  of  several  cannon  at  a  common  object  may 
greatly  increase  their  effect.  A  similar  advantage  follows 
in  mines. 

The  primers  are  of  two  general  classes: 

I.  High  tension,  in  which  ignition  results  from  the  pass- 
age of  the  electric  spark  between  the  disconnected  ends 


XVIII. — MEANS   OF    COMMUNICATING    FIRE.  5 

of  two  insulated  conductors.  For  this  class  the  conductors 
require  careful  insulation  and  to  be  separated  from  adjacent 
circuits,  so  as  to  prevent  the  primers  in  one  circuit  from 
being  accidentally  exploded  by  currents  induced  from  the 
other  circuits. 

2.  Low  tension^  in  which  ignition  results  from  the  heating 
of  a  short  wire  of  high  resistance  which  connects  the  ends 
of  the  conductors.  Owing  to  the  ease  with  which  the  con- 
dition of  the  circuit  can  be  tested  before  firing,  and  the 
comparatively  low  electro-motive  force  of  the  currents 
employed,  this  is  the  only  class  of  electric  primer  used 
in  artillery. 

Figure  5  represents  a  common  electric  primer,  and  figure 
6  an  obturating  electric  primer.  The  platinum  wire  is 
coiled  to  facilitate  its  handling  in  manufacture.  It  is  sur- 
rounded by  a  wisp  of  gun-cotton. 

The  obturating  plug,/,  of  hard  rubber  seals  the  channel 
by  being  pressed  against  the  sharp  ring  in  rear.  In  other 
essentials  these  primers  resemble  figures  2  and  4:. 

MEANS   OF   IGNITING    PRIMERS. 

If  quick  match  be  used  it  sufiices  to  unite  the  lines  so 
that  the  distances  B  C,  B  C,  B  C\  etc.,  in  figure  7;  or 
BC^  B  D  C,  figure  8,  be  equal.  If  the  detonating  tubes, 
page  2  be  used,  these  precautions  are  unnecessary. 

For  electric  primers  the  voltaic  battery  is  generally 
employed,  although  for  experimental  purposes  a  small 
portable  dynamo  or  frictional  apparatus  is  very  convenient. 

When  it  is  desired  to  be  able  to  fire  without  delay,  a 
battery  is  preferred,  which,  like  the  Leclanche,  can  be  kept 
for  a  long  time  in  open  circuit  without  sensible  change  and 
which  only  needs  the  circuit  to  be  closed  to  produce  the 
effect  desired. 

In  using  the  electric  current  in  direct  or  continuous  circuit 


6  XVIII  — MEANS   OF    COMMUNICATING    FIRE. 

as  in  figure  9,  the  number  of  cells  of  the  battery  required 
increases  with  the  number  of  primers, /,/',/",  and  it  may 
happen  that  the  most  sensitive  of  the  primers,  exploding 
first,  will  cause  the  remainder  to  fail. 

For  the  second  reason  a  derived,  or  parallel  circuit,  as 
in  figure  10,  is  preferred.  The  successive  explosion  of  the 
more  sensitive  primers  increases  the  current  which  passes 
through  each  of  the  remaining  primers,  since  their  number 
is  diminished. 

In  order  to  employ  a  weaker  battery,  the  arrangement 
shown  in  figures  11  and  12,  serves,  by  sweeping  the  key,  ky 
over  the  ends  of  the  terminals,  to  produce  a  practically 
simultaneous  discharge. 

CLASS   II. 

FUZES. 

Fuzes  are  employed  to  explode  the  bursting  charge  of  a 
projectile  at  any  desired  point  of  its  trajectory.  They  may 
be  classified,  according  to  their  mode  of  operation,  as  timey 
impact  and  combination  fuzes. 

I.    TIME    FUZES. 

A  time  fuze  contains  a  column  of  com.position,  which, 
having  been  ignited  at  the  discharge  of  the  piece,  after  having 
burned  for  a  definite  time,  ignites  the  bursting  charge. 

Requisites. 

Such  fuzes  are  principally  employed  to  burst  projectiles 
while  in  the  air;  they  therefore  require  that  the  relation  be 
known  between  the  distance  to  the  point  of  explosion  and 
the  time  of  flight,  and  that  the  column  be  taken  of  such  a 
length  that  it  will  burn  in  the  time  so  determined. 

The  first  of  these  requisites  involves  the  estimation  of  the 
distance  by  various  systems  of  range  finding,  and  the  deter- 


XVIII. — MEANS   OF   COMMUNICATING    FIRE.  7 

mination  from  Ballistics  of  the  required  angle  of  projection 
and  the  time  of  flight  to  the  point  desired.  The  second 
requirement  demands  that  the  rate  of  burning  be  known, 
and,  since  the  time  of  burning  is  varied  by  varying  the 
length  of  the  column,  that  the  rate  be  uniform  throughout 
its  length.  Finally,  that  the  column  be  taken  of  the  exact 
length  required  by  the  rate,  and  that  it  both  receive  and 
impart  fire  with  certainty. 

The  principal  points  to  be  considered  in  the  development 
of  time  fuzes  are,  that  as  we  increase  the  muzzle  velocity 
and  sectional  density  of  our  projectiles,  the  longer  will  be 
the  maximum  time  of  burning  required  for  the  fuze.  As 
the  remaining  velocity  increases,  the  greater  will  be  the  error 
in  distance  due  to  a  given  error  in  time;  and  the  greater  the 
range,  the  more  difficult  will  it  be  to  detect  the  error  in 
distance.  Therefore  improvements  in  cannon  require  corre- 
sponding improvements  in  the  uniformity  of  rate  and  in  the 
exactness  of  the  length  of  the  burning  column.  The  greater 
the  rate  of  burning,  the  larger  the  scale  and  therefore  the 
smaller  the  effect  of  a  given  error  in  cutting. 

The  rate  is  so  much  affected  by  the  conditions  relating  to 
the  resistance  of  the  air  during  flight,  that,  while  uniformity 
of  rate  may  be  indicated  by  the  tests  of  manufacture,  the 
lengths  of  column  for  given  ranges  should  be  determined  by 
actual  trial  in  the  gun.  On  this  account,  and  to  avoid  com- 
putation in  the  field,  when  the  initial  velocity  and  sectional 
density  are  fixed,  the  scale  is  preferably  one  of  ranges,  in- 
stead of  units  of  time. 

The  great  efficiency  of  projectiles  properly  exploded  in 
air,  as  explained  in  Chapter  XVI,  and  the  experience  gained 
with  smooth-bore  cannon,  in  which  this  was  the  only  form 
of  fuze  that  could  be  successfully  used,  account  for  the  pains 
that  have  been  taken  to  meet  these  requirements  ever  since 
the  early  days  when  the  fuze  was  lighted  before  loading. 


8  XVIII. — MEANS   OF   COMMUNICATING    FIRE. 

Kate  of  Burning. 

This  will  depend  upon  the  conditions  named  Chapter 
VIII,  page  3. 

The  rate  was  formerly  varied  by  varying  the  composition, 
but  as  any  departure  from  the  usual  proportions  is  found 
to  diminish  the  uniformity  of  the  rate,  to  increase  the 
difjficulty  of  preservation,  and  to  increase  the  amount 
of  residue,  it  is  now  thought  best  to  vary  the  rate  only 
by  varying  the  amount  of  incorporation  and  the  density 
of  the  composition. 

When  the  total  time  of  burning  is  very  great,  as  in  some 
of  the  large  mortar  projectiles,  which  may  be  40  seconds 
in  the  air,  a  return  to  the  variable  composition  appears 
necessary. 

Former  Practice. 

For  spherical  projectiles  the  column  was  cylindrical  and 
was  ordinarily  contained  in  a  conical  case  of  paper,  wood  or 
metal.  This  was  filled  with  small  successive  quantities  of 
mealed  gunpowder  which  were  compacted  by  a  drift  upon 
which  a  given  number  of  blows  were  struck  by  a  mallet.  By  a 
repetition  of  the  process  the  case  was  gradually  filled. 

The  exterior  of  the  case  was  divided  into  equal  propor- 
tionate parts  by  which  to  regulate  the  time  of  burning, 
either  by  cutting  off  the  case;  or,  since  the  entire  column 
might  then  be  dislodged  backward  into  the  cavity  of  the 
shell  by  the  shock  of  discharge,  by  boring  into  it  with  a 
gimlet. 

The  fuze  was  ignited  by  a  priming  of  mealed  powder 
placed  so  as  to  catch  fire  from  the  flame  passing  through 
the  windage  of  muzzle-loading  guns,  both  smooth-bore  and 
rifled. 

The  method  of  filling  caused  variation  in  fuzes  of  the  same 
kind,  and  even  between  different  sections  of  the  same  fuze. 


\         XVIII. — MEANS   OF   COMMUNICATING    FIRE.  9 

1  '  ~ 

\ 

Exv.mples  of  Fuzes  for  Muzzle-loading  Projectiles, 

Figures  13  and  14  illustrate  two  varieties  of  time  fuze,  in 
one  of  wUch  the  composition  was  fixed  in  the  case  and  in 
the  other  v^as  movable. 

The  Mortar  fuze  case  or  plug  was  made  of  a  close  grained 
wood,  like  beech,  bored  out  nearly  to  the  bottom.  The 
top  of  the  cavity  was  enlarged  to  receive  the  priming  of 
mealed  powder  and  alcohol.  This  was  covered  by  a  cap 
of  waterproof  paper  on  which  was  marked  the  rate  of  burn- 
ing. For  economy  of  manufacture  the  exterior  of  all 
mortar  fuze  plugs  was  marked  in  inches  and  tenths,  instead 
of  with  reference  to  the  rate  of  burning  of  their  contents. 

The  Sea  Coast  fuze  consisted  of  a  brass  plug  containing 
a  separate  paper  case,  filled  with  a  composition  of  variable 
proportions  and  bearing  on  its  exterior  a  scale  of  times. 
The  mouth  of  the  plug  was  closed  by  a  water-cap,  per- 
forated by  a  zig-zag  channel.  This  was  also  filled  with 
mealed  powder  for  the  ignition  of  the  fuze;  but  was  so 
constructed  as  to  prevent  the  composition  from  being 
extinguished  in  the  ricochet  fire  over  water,  largely  em- 
ployed in  former  times. 

These  fuzes  answered  well  for  the  comparatively  low 
remaining  velocities  and  short  ranges  usual  when  spherical 
projectiles  were  employed;  but  they  required  valuable  time 
for  their  adjustment  and  were  imperfectly  protected  from 
the  effects  of  excessive  heat  or  of  moisture  while  in  store. 

The  Bormann  fuze,  figure  15,  was  invented  to  overcome 
these  and  other  objections.  The  case  being  of  pewter  is  un- 
altered in  size  by  meteorological  changes,  and  it  contains 
the  composition  in  a  channel,  which,  though  air  tight,  can 
be  readily  cut  by  a  proper  tool.  The  circular  form  of  the 
column  and  its  diminished  section  allow  the  size  of  the  case 
to  be  reduced,  and  the  composition  to  be  compressed  in  the 
direction  of  its  shortest  dimension.     The  mean  density  of 


10  XV^I. — MEANS   OF    COMMUNICATING    FIRE. 


the  succe^ssive  layers  estimated  in  the  direction  of  the  com- 
bustion is  thereby  made  uniform.  The  case  is  screwed  into 
the  fuze  hole  by  a  screw  driver,  the  prongs  of  whxh  engage 
into  the  recesses  a,  a. 

The  graduated  arc  lies  over  the  circular  column  of 
mealed  powder  which,  after  compression,  is  covered  by  the 
tightly  fitting  wedge  shaped  ring,  b.  The  only  outlet  to 
the  channel  is  under  the  zero  of  graduation;  this  outlet,  r, 
and  the  magazine^  m,  are  filled  with  fine  powder  which  is 
retained  by  a  disc  of  tin,  e. 

To  enable  the  fy^e  to  resist  the  shock  of  discharge,  to 
which  its  softness,  density  and  form  render  it  especially 
weak;  and  also  to  increase  the  effect  of  a  small  bursting 
charge,  the  lower  portion  of  the  fuze  hole  is  closed  by  a 
perforated  disc,/. 

The  objections  to  the  Bormann  fuze  are  the  short  time 
of   its   burning;    the   uncertainty  of  its  ignition  unless  it 
be  carefully  primed,  and  that,  once  set  for  firing,  it  is  use- 
less for  any  greater  time  of  flight. 
Present  Time  Fuse. 

The  use  of  breech-loading  cannon  necessarily  prevents 
the  ignition  of  the  fuze  through  the  windage  so  that  a  special 
device  called  an  inertia  igniter  is  employed  for  that  pur- 
pose.    Its  operation  is  illustrated  in  figures  16  and  24. 

In  figure  16  the  inertia  igniter  consists  of  a  mass  of  lead 
containing  a  pellet  of  fulminate  and  supported  a  short  dis- 
tance above  the  sharp  point,  /,  by  some  device  which,  while 
stable  against  ordinary  shocks,  will  be  surely  moved  by  that 
of  discharge.  This  device  may  be  either  a  spiral  spring  or  a 
transverse  pin  of  brittle  material. 

The  flame  from  the  fulminate  escapes  through  the  holes^ 
h,  into  the  annular  cavity,  r,  and,  by  a  hole  on  the  inner 
surface  of  the  ring,  r,  ignites  the  circular  column  of  com- 
position which  the  rmg  contains. 


XVIII. — MEANS   OF    COMMUNICATING    FIRE.  11 

The  exterior  surface  of  the  ring  is  graduated,  as  in 
seconds,  and  the  body  of  the  fuze  contains  a  mark,  placed 
opposite  to  the  entrance  to  the  magazine,  w,  so  that  by- 
setting  the  ring  before  firing  with  any  division  of  its  scale 
opposite  to  the  mark,  the  length  of  the  burning  column  is 
fixed.     The  cap,  k,  is  used  to  c^amp  the  ring  in  place. 

To  prevent  the  opposing  rush  of  the  gases  from  the  two 
sections  of  the  burning  column,  it  is  ignited  at  one  of  its 
ends;  this  permits  a  free  escape  of  the  gases  to  the  outer 
air  through  a  hole  previously  temporarily  sealed  against 
moisture. 

Figure  17  shows  the  course  taken  by  the  escaping  gases 
when  the  burning  surface  moves,  as  in  the  Bormann  fuze, 
in  two  directions  from  the  hole,  ^,  to  the  magazine,  m^ 
Figure  18  shows  the  improved  method. 

For  long  ranges,  since  the  form  of  the  projectile  permits 
its  length  to  be  indefinitely  increased,  the  fuze  may  contain 
two  or  more  rings  arranged  in  tiers. 

II.   IMPACT    FUZES. 

Concussion  Fuzes. 

Until  the  introduction  of  rifled  projectiles  many  unsuc- 
cessful attempts  were  made  to  combine  the  time  fuze  with 
some  device  which  would  be  safe  when  the  gun  was  fired; 
and  yet,  if  the  time  fuze  failed  to  act  at  the  proper  point, 
would  explode  the  bursting  charge  on  impact. 

Owing  to  the  uncertainty  of  the  direction  of  the  impact 
such  fuzes  are  called  concussion  fuzes  to  distinguish  them 
from  the  percussion  fuzes  now  generally  employed. 
Percussion  Fuzes. 

Although  as  stated,  Chapter  XVI,  page  21,  the  shock  of 
impact  may  in  certain  cases  suffice  to  explode  the  bursting 
charge,  it  is  much  more  certain  to  employ  a  special  appa- 
ratus for  this  purpose. 


12  XVIII. — MEANS   OF    COMMUNICATING    FIRE. 


Although  more  complicated  in  structure  than  time  fuzes, 
those  of  the  percussion  class  act  with  more  certainty  since 
the  conditions  to  be  fulfilled  are  more  easy  of  accomplish- 
ment. They  are  not  as  subject  to  deterioration  in  store, 
and,  since  they  are  usually  entirely  automatic,  they  require 
no  preparation  before  firing.  By  the  volume  of  smoke 
resulting  from  the  explosion  of  shells  containing  percussion 
fuzes,  the  gunner  is  afforded  one  of  the  readiest  means 
of  correcting  his  aim. 

Percussion  fuzes  are  divided,  according  to  their  position 
on  the  projectile,  into  fronts  or  base  fuzes.  The  former 
possess  the  advantage  that  on  impact,  the  bursting  charge  is 
thrown  towards  the  fuze  ;  the  latter  class  is  required  for  pro- 
jectiles to  be  used  against  armor. 
Requisites. 

A  good  percussion  fuze  requires — 

1.  A  case  to  hold  and  guide  the  movable  parts,  and  to 
protect  them  from  being  clogged  by  the  dust  arising  from 
the  bursting  charge  in  transportation,  and  by  the  earth 
against  which  they  may  strike. 

2.  A  plunger,  by  the  motion  of  which,  on  impact,  the 
charge  is  fired. 

3.  A  fulminating  composition,  ignited  by  the  plunger. 

4.  The  priming,  a  charge  of  fine  powder  ignited  by  the 
fulminate  and  serving  to  increase  the  certainty  of  the 
ignition  of  the  bursting  charge. 

5.  A  safety  device,  by  which  the  accidental  dislodgement 
of  the  plunger  is  prevented;  but  which  will  certainly  free 
the  plunger  when  the  piece  is  fired. 

6.  A  device  to  prevent  the  plunger  from  moving  forward 
in  its  cavity  during  flight.  This  tendency  results  from  the 
greater  retardation  of  the  projectile  than  of  the  enclosed 
plunger  by  the  resistance  of  the  atmosphere.  The  effect 
of  this  relative  motion  may  be  to  cause  a  premature  explo- 


XVllt.— MeA^§  of  COMMtJi^lCAftNG   FIRE.         '     13 

sion  if  the  fulminate  is  sensitive;  or  else  on  impact  to 
deprive  the  plunger  of  sufficient  motion  to  cause  the  explo- 
sion of  a  fulminate,  the  sensitiveness  of  which,  for  the  reason 
above  given,  has  been  diminished. 

The  most  difficult  of  these  requisites  to  provide  is  the 
safety  device.  In  the  early  percussion  fuzes  the  plunger 
was  a  single  mass  sustained  by  a  transverse  pin  or  by  lugs 
cast  upon  it.  The  pin  was  made  strong  enough  to  stand  the 
shocks  of  transportation;  but  was  shorn  off  by  the  shock  of 
discharge.  The  mass  to  be  given  to  the  plunger  was  determ- 
ined by  confficting  considerations.  If  made  so  light  as  not 
to  be  liable  to  shear  its  support  by  accident,  it  might  fail 
to  explode  the  fulminate  when  impact  occurred  at  a  low 
velocity.  The  advantage  of  a  proper  distribution  of  func- 
tions among  the  parts  of  the  apparatus  appears  from  the 
following  discussion: 
Type  of  Improved  Percussion  Fuze. 

Let  Fhe  the  initial  velocity  of  the  projectile  and  v,  and 
z;',  its  velocities  on  impact,  and  after  impact,  as  in  the 
ricochet. 

Let  m,  be  the  mass  of  the  plunger  and  p/  that  of  the 
safety  device:  this  we  will  suppose  to  be  a  hollow  cylinder 
as  in  figure  19,  surrounding  the  upper  part  of  the  plunger, 
but  kept  from  moving  backward  upon  it  by  a  suitable  pro- 
jection, as  that  upon  the  flat  spring,  s\  In  the  type  selected 
the  section  of  the  plunger  is  square  and  fits  the  hole  in  the 
safety  device. 

When  the  piece  is  fired,  m'  moves  relatively  to  the  rear 

with  an  energy  which,  on  account  of  the  large  value 

2i 
of  Vj  is  capable  of  overcoming  a  resistance  great  enough  to 
be   absolutely  safe    against   all   accidents  of  transportation. 
In  so  doing  it  becomes  solidly  united  to  m,  so  that  when 
impact  occurs,  although  v—v'  may  be  much  less   than  F", 


14  Xvm.— MEANS   OF   COMMUNICATING    FIRE. 


the  energy  — - —    {v—v'Y  may  easily  overcome  the  resist- 

ance  of  the  spiral  springs,  and  so  ignite  the  fulminate,/, 
and  the  priming,/. 

If,  during  the  flight  of  the  projectile  m'  does  not  remain 
relatively  at  rest  its  conical  form  tends  to  make  it  roll 
rather  towards  the  base  of  the  cavity  than  away  from  it.  It 
is  also  urged  in  this  direction  by  the  spring  s. 

This  fuze,  which  is  of  French  origin,  represents  one  of 
the  best  existing  types.  It  requires  a  value  of  V  not  less 
than  about  1000/.  ^.,  and  therefore  is  somewhat  more  com- 
plicated in  construction  when  projectiles  containing  it  are 
fired  with  low  velocities. 

Percussion  Fuzes  used  in  the  United  States. 

Hotchkiss  Front  Percussion  Fuze.     Figure  20. 

A,  is  the  case,  closed  in  front  by  the  screw-cap  B,  and 
with  a  conical  hole  in  rear  closed  by  a  lead  safety  plug  C. 
Dy  represents  the  plunger,  composed  of  lead  cast  into  a 
brass  jacket  to  prevent  its  dilatation  by  shock, 

A  continuous  brass  wire,  E,  the  upper  portion  of  which 
is  bent  in  a  semi-circle  concentric  with  the  plunger,  is  cast 
into  the  lead  and  supports  the  plunger  in  the  case.  The 
lower  ends  of  the  wire  are  securely  held  by  the  friction 
of  the  safety  plug  against  the  sides  of  its  cavity.  At  7%  is 
the  fulminate,  and  at  F,  the  priming. 

When  the  piece  is  fired,  C,  is  dislodged  backward  into 
the  interior  of  the  cavity  either  by  its  own  inertia  or  by  the 
blow  received  from  F).  The  wires  spread  outward  and 
prevent  the  plunger  from  moving  forward  until  the  pro- 
jectile strikes  a  sufficiently  resisting  object. 

Hotchkiss   Base   Percussion   Fuze.      Figure   21. 

The  case.  A,  carries  the  fulminate,  F,  in  a  large  percus- 
sion cap  contained  in  the  perforated  screw-box^  which  is 


XVIII.— MEANS   OF   COMMUNICATING    FIRE.  15 

formed  in  two  sections,  G  and  JI.  The  base  of  the  case  is 
provided  with  a  projecting  flange,  /,  brought  to  a  thin  edge 
which,  when  the  fuze  is  screwed  home,  acts  as  a  gas  check. 
The  plunger  Z>,  is  made  as  in  figure  20,  but  contains  a 
central  firing-pin,  Z,  roughened  so  that  it  will  hold  well 
in  the  lead. 

The  rear  end  of  the  firing-pin  projects  beyond  the  bottom 
of  the  plunger,  while  its  front  end  is  sunk  a  little  below  the 
surface  so  that  when  this  compound  part  {D  and  L)  is  in 
place,  it  is  prevented  from  moving  by  the  screw-box. 

When  the  gun  is  fired  the  plunger  slides  back  on  the 
firing-pin  so  that  the  point  projects  above  the  plunger. 
The  lead  being  soft,  and  being  prevented  from  expanding 
by  the  jacket,  it  takes  a  fresh  hold  on  the  pin  and  supports 
it  when  it  is  thrown  forward  on  impact. 

This  fuze  has  certain  structural  defects  which  render 
its  operation  less  certain  than  that  of  the  front  fuze.     For 
its  special  purpose  it  is  probably  one  of  the  best  known. 
Krupp  Fuze. 

Figure  22  shows  a  Krupp  fuze  in  a  double  walled  shell. 
Safety  in  loading  results  from  the  transverse  pin,  /,  which, 
with  the  screw-box  containing  the  fulminate,  is  inserted  just 
before  loading.  The  rotation  of  the  projectile  expels  the 
pin,  leaving  the  longitudinal  pin,/,  free  to  be  driven  inward 
on  impact  so  as  to  prevent  the  entrance  of  earth  into  the 
cavity  of  the  fuze.  The  nomenclature  of  figure  22  is  the 
same  as  that  of  figures  20  and  21.  It  is  said  that  this 
pattern  is  to  be  replaced  by  one  containing  a  safety  device 
which  is  intended  to  be  unscrewed  by  the  rotation  of  the 
projectile. 

III.    COMBINATION    FUZES. 

These  combine  the  principles  of  the  time  and  impact  fuzes 
50  as; — 


16  XVIII. — MEANS   OF   COMMUNICATING    FIRE. 

1.  To  increase  the  probability  of  explosion;  since,  if  the 
probability  of  a  failure  in  each  of  the  two  cases  be,  say,  0.01; 
that  of  the  combination  will  be  0.0001. 

2.  To  permit  the  character  of  the  firing  to  be  rapidly 
varied, 

3.  To  increase  the  certainty  of  explosion  when  the  pro- 
jectile is  fired  with  a  low  velocity. 

Figure  23  illustrates  one  of  the  most  recent  combination 
fuzes  used  in  the  French  service. 

^  is  a  leaden  fuze  tube  made  as  d^escribed  page  2.  It  is 
wrapped  spirally  about,  and  secured  to  the  hollow  cone,  C; 
this  is  held  in  place  by  the  clamp  screw,  D.  The  lower  end 
of  the  fuze  tube  communicates  through  the  priming,  /*,  with 
the  cavity  in  which  lies  the  percussion  fuze  described  page  13. 

The  inertia  igniter  consists  of  a  loose,  pointed  piston,  ZT, 
which,  until  the  instant  of  discharge,  is  separated  from  the 
fulminate,  F^  by  the  spiral  springs  .S". 

K^  is  a  conical  cap  pierced  with  a  series  of  numbered  holes 
corresponding  to  the  times  of  burning  and  provided  with  a 
vernier  for  interpolating  a  puncture  between  any  two  holes. 
The  puncture,  owing  to  the  softness  of  the  metal  of  which  (7, 
is  composed,  is  made  entirely  through  both  its  walls. 

When  the  piece  is  discharged,  the  washer  of  compressed 
powder,  W^  is  ignited  by  ZT,  and  through  the  puncture  the 
fire  extends  to  the  composition  in  E.  At  the  same  time  the 
percussion  fuze  acts  as  before  described. 

But  for  the  union  of  the  two  fuzes  in  the  same  case,  which 
the  construction  of  the  projectile  and  the  operation  of  front 
percussion  fuzes  requires,  this  fuze  illustrates  the  principle 
referred  to  Chapter  XVI,  page  34.  The  simplicity  of  con- 
struction, which  was  formerly  considered  of  prime  impor- 
tance, has  been  entirely  subordinated  to  efficiency  of  oper- 
ation, notwithstanding  the  greatly  increased  cost  which  this 
involves. 


XVIII. — MEANS   OF   COMMUNICATING    FIRE.  17 

The  Flagler  Combina^tion  Fuze.    Figure  24. 

This  fuze,  devised  by  Colonel  Flagler  of  the  Ordnance 
Department,  is  now,  1889,  undergoing  trial.  It  combines 
many  of  the  principles  just  discussed  and  adds  two  new 
features  to  provide  for  the  requirements  numbered  5  and 
6,  page  12. 

The  first  feature  consi^s  of  a  copper  wire,  d^  screwed  from 
the  rear  into  the  open  end  of  the  screw-cap^  A.  The  lower  end 
of  this  wire  is  bent  at  right  angles  so  as  to  support  firmly 
the  leaden  time  plunger,  D.  Just  below  the  screw  thread 
by  which  it  is  suspended  the  diameter  of  the  wire  is  reduced 
to  any  desired  extent. 

The  wire  is  broken  at  the  neck  so  formed  by  the  stress 
due  to  the  acceleration  of  the  projectile,  both  in  translation 
and  in  rotation.  The  latter  stress,  occurring  only  when  the 
piece  is  fired  increases  the  certainty  of  ignition  without 
diminishing  the  safety  of  the  apparatus  against  accidental 
shock. 

On  firing,  the  mass,  Z>,  is  thrown  against  the  fixed  firing 
pin,  F^  and  the  fulminate  ^^,  is  ignited.  The  flame  from 
the  fulminate  escapes  through  the  radial  holes  and  the  an- 
nular channel,  ^,  b^  to  the  end  of  the  column  of  composition 
projecting  into  the  radial  groove,  Z,  formed  on  the  lower 
side  of  the  ring,  or  carcass  C.  The  gas  first  formed  blows 
off  the  vent  cover,  ^,  and  allows  the  remaining  gases  to 
escape  freely. 

When  the  column  has  burned  to  the  point,  b\  corre- 
sponding to  which  there  is  a  fixed  mark  on  that  portion 
of  the  body  next  to  the  graduation  on  the  ring,  the  priming 
K^  is  ignited  and  the  flame  from  it  passes  down  the  fluted 
surfaces  of  the  members,  G^  H^  7,  of  the  percussion  fuze 
into  the  bursting  charge. 

The  advantage  claimed  for  this  safety  device  over  those 
in  which  ears  projecting  from  the  mass  Z>,  are  shorn  off  by 


IS  XVIII. — MEANS   OF   COMMUNICATING    FIRE. 

the  shock  of  discharge,  refers  to  the  uniformity  of  copper 
wire  and  to  'the  absence  of  the  loose  pieces,  which,  after 
shearing  has  occurred,  may  impede  the  action  of  the 
plunger. 

The  percussion  fuze  resembles  the  Hotchkiss  base  fuze, 
with  the  following  advantages: — 

1.  The  priming  K,  which  serves  for  both  fuzes  of  the 
combination,  makes  the  volume  of  the  flame  on  impact 
much  greater  than  when  fulminate  only  is  employed. 

2.  In  order  to  fulfil  requirement  6,  page  12,  a  disc  of  thin 
zinc  separates  the  point  of  the  firing  pin,  h,  from  the  fulmi- 
nate above  it.  This  presents  a  positive  and  uniform 
resistance  to  premature  explosion;  and,  since  a  pressure  of 
6  pounds  is  required  to  pierce  it,  the  fulminate  may  be 
made  as  sensitive  as  may  be  desired. 

3.  On  impact  the  powder  is  thrown  toward  the  fuze. 
The  fuze  works  well  in  practice.    The  percussion  fuze 

was  found  to  operate  when  the  projectile  was  fired  through 
a  2-inch  board,  though  it  failed  in  penetrating  a  board  one 
inch  thick.  It  is  thought  that  it  will  explode  on  striking 
animate  objects  or  sandy  or  marshy  ground. 

GENERAL  REMARKS. 

Owing  to  their  greater  permanency  of  form  in  store,  and 
their  diminished  volume,  metallic  cases  are  preferred  to  the 
wooden  ones  formerly  employed. 

In  order  to  cheapen  the  manufacture,  which  at  best  is 
very  expensive,  the  parts  are,  whenever  possible,  made  of 
pewter,  cast  in  metallic  molds  into  finished  forms.  When 
strength  and  infusibility  are  required,  brass  or  bronze  are 
used,  cast  as  described  in  Chapter  XVII. 

To  prevent  unscrewing  during  flight,  the  screw  thread  of 
base  fuzes  should  turn  in  a  direction  contrary  to  that  of 
the  rifling. 


3tvni. — MEANS  O^  COMMttNlCATiNG   f'lRE.  19 


It  takes  an  appreciable  time  after  impact  for  tLe  explo- 
sion to  occur;  so  that  even  when  the  fulminate  was  pur- 
posely ignited  by  the  shock  of  discharge,  the  shell  did  not 
burst  until  it  had  gone  several  yards  beyond  the  muzzle  of 
the  gun.  This  is  of  importance  in  understanding  the  effect 
of  shrapnel  fire  with  percussion  fuzes,  and  serves  to  show 
that  explosions  within  the  gun  generally  result  from  defects 
in  the  construction  of  the  projectile. 

To  prevent  premature  explosion  from  the  plunger's 
being  thrown  violently  forward  by  the  elasticity  of  the 
bottom  of  the  shell,  on  discharge,  a  perforated  cardboard 
washer  is  often  required. 

A  percussion  shell,  unexploded  in  experimental  firing 
should  never  be  tampered  with:  if  possible,  it  should  be 
exploded  on  the  spot  by  a  dynamite  cartridge. 


X15t. — GDN  CoKstktrcTioN. 


CHAPTER  XIX. 

GUN  CONSTRUCTION. 

Nomenclature  of  Stresses. 

The  total  pressure  of  the  powder  gases  in  a  gun  may  be 
analyzed  as  follows  with  reference  to  the  direction  of  the 
resulting  strains. 

1.  A  radial  stress,  known  by  the  special  name  of 
"pressure"  (/). 

2.  A  tangential  stress,  or  hoop  tension  (/)  which  tends 
to  split  the  piece  open  longitudinally,  being  similar  in  its 
action  to  the  force  which  bursts  the  hoops  of  a  barrel. 

3.  A  longitudinal  stress  ((/)  which  tends  to  pull  the  piece 
apart  in  the  direction  of  its  length. 

4.  Besides  these,  which  are  the  principal  stresses  now 
considered,  was  formerly  treated  the  transverse  stress  which 
tends  to  bend  outward  the  staves  of  which  the  tube  may  be 
supposed  to  consist. 

Its  effects  are  so  closely  associated  with  the  strains  above 
named  that  it  is  no  longer  discussed. 

Of  the  principal  stresses  named  the  most  important  is  the 
tangential,  since  it  is  that  from  which  failure  most  readily 
occurs. 

BARLOW'S  LAW. 
Limitations. 

This  law,  which  was  until  recently  applied  to  the  con- 
struction of  homogeneous  cannon,  if  confined  to  stresses 
beneath  the  elastic  limit,  (Chap.  XV,  p.  11,)  under  which 


XIX. — GUN   CONSTRtJCTIOl^. 


limit  the  stresses  are  taken  to  be  proportional  to  the  strains, 
gives  results  which  agree  fairly  well  with  those  obtained  by 
the  more  exact  methods  now  generally  employed. 

But,  when  applied  to  built  up  guns  composed  of  concentric 
cylinders  assembled  by  shrinkages  as  described  in  Chap.  XV, 
it  is  no  longer  generally  used  because  it  does  not  analyze 
the  resultant  strain  into  the  component  strains  occuring  in 
three  coordinate  directions.  For  example,  if  we  compress  a 
cube  in  the  direction  of  the  axis  of  Z,  there  will  be  deyeloped 
along  the  axes  of  X  and  Y  component  strains  correspond- 
ing to  tensile  stresses  acting  in  each  of  these  directions  and 
conversely. 

On  account  of  the  relative  simplicity  of  Barlow's  law  it 
will  be  employed  to  illustrate  the  general  principles  of  gun 
construction.  A  more  extended  discussion  of  the  theory  now 
accepted  will  be  found  in  the  appendix  of  this  chapter. 


DEDUCTION    OF    BARLOW's    LAW. 

Hypotheses. 

Suppose — {a)  the  piece  to  be  a  hollow  cylinder  of  homo- 
geneous metal,  and — {h)  that  the  effect  of  a  central  force  be 
transmitted  outward  in  such  a  manner  as  to  make  constant 
the  area  of  cross-section  by  a  plane  perpendicular  to  the 
axis. 

{a)  The  homogeneity  of  the  metal  Is  required,  so  that  a 
constant  relation  may  exist  between  stress  and  strain  ;  or  that 
the  coefficient  of  elasticity,  known  herein  as  E^  may  remain 
constant. 

{h)  The  constancy  of  area  or  cross-section  resembles 
the  assumption  that  the  various  stresses,  from  the  effects  of 
which  the  physical  properties  of  the  metal  are  determined 
in  the  testing  machine,  continue  to  be  applied  to  the  original 


XIX. — GUN    CONSTRUCTION. 


area  of  cross-section ;  although  it  is  evident  that,  if  the  volume 
of  the  metal  be  constant,  its  area  of  cross-section  must 
diminish  or  increase  when  exposed  to  tensile  or  compressive 
stress  respectively.* 

Wertheim's  experiments  show  that  the  developed  strains 
are  each  —  ^  of  the  principal  strain. 
Preliminary  Statement. 

Suppose  that  figure  1  represents  a  section  of  a  homogen- 
eous gun  after  firing:  the  radii  R  and  >^' having  been  ex- 
tended to  r  and  J^"  so  as  to  maintain  the  sectional  area 
constant. 

Then,  the  area  whose  limiting  radii  are  r  and  E'  being 
common  to  both  states  of  the  section,  we  have 
TT  (r^  _  i?^)  rr  TT  {R"  »  —  R' '),     or 
(r  J^R){r—R)  =  {R"  +  R')  {R"  —  R'), 

But  since  R"  and  R'  are  each  greater  than  either  R  or  r 
R"  +  R'y  r-\-R 

,'.r—RyR"^R',    or 

2TT{r—R)__r—R       R"  —  R' 
27rie       ~".      i?      -^         R' 

The  two  members  of  this  inequality  measure  the  strains 
on  the  interior  and  exterior  surfaces  respectively,  so  that  it 
appears  that  the  surface  of  the  bore  might  be  strained  be- 
yond its  elastic  limit  before  that  of  the  outside  layers  was 
reached. 

The  resulting  set,  if  slight,  might  destroy  the  accuracy  of 
the  piece  from  the  dilatation  of  the  bore;  and,  if  consider- 
able, it  might  lead  to  the  formation  of  fissures  which  would 


*Throughout  the  following  discussion  we  will  consider  that  we  are 
dealing  with  a  cylinder  of  but  one  unit  of  length,  since,  as  the  length  of 
the  cylinder  varies,  both  the  pressure  tending  to  burst  the  cylinder  and 
the  resistance  which  it  opposes  will  vary  in  the  same  ratio. 


XIX. — GUN    CONSTRUCTION. 


facilitate  the  final  rupture  in  detail  of  the  successive  cylin- 
drical layers  of  which  the  gun  may  be  supposed  to  consist* 
The  considerations  explain  the  statement  in  Chapter  V, 
as  to  strength  vs.  weight. 

Analysis. 

To  determine  the  law  by  which  the  tangential  stresses 
are  distributed  throughout  the  section  of  a  gun: — 

Let  J^  and  Z  be  the  radius  and  the  circumference  of  the 
bore.  Let  /<,  be  the  radial  pressure  per  unit  of  area  and 
T  the  tangential  stress  on  the  surface  of  the  bore.  Let  r,  Zy 
p  and  /  represent  the  same  quantities  on  any  exterior 
cylindrical  surface,  the  area  of  cross-section  between  which 
and  Z  is  A.     Then  by  assumption,  {fi)  above 

Tt  {f— B})  ::^  A,     and     .*.     rdr  =  RdR. 

Multiplying  the  first  member  of  the  last  equation  by  -, 

and  the  second  member  by  -^  we  have  r^  —  =  i?^  -^ . 

''  R  r  R 

I     But,  since  the  ratio  between  the  circumference  and  the 

radius  is  constant,  and  since  beneath  the  elastic  limit  the 

stresses  are  proportional  to  the  strains 

,  dr        dz  t         .  dR         T 

i  -  =  V  =  ^  ""^  ■:ff  =  ■:£ 

Therefore,  we  have 

tf^        TR^        ,       TR^ 

_  =  — or/=-^  (1) 

Or,  since  under  given  conditions  of  /o?  ^  and  i?,  TR^ 
will  be  constant,  the  tangential  stress  {or  strain)  on  each  sue- 


*  This  last  statement,  though  generally  true,  is  subject  to  modification 
depending  on  the  ductility  of  the  material  and  the  development  of  special 
elasticity.     See  post. 


XIX. — GUN    CONSTRUCTION. 


cessive  concentric  elementary  cylinder  varies  inversely  with  the 
square  of  its  radius. '   This  is  Barlow's  law. 

This  condition  may  be  represented  by  figure  2,  in  which 
the  ordinates  of  the  curve  T  T'  represent  the  tangential 
stresses  on  the  corresponding  circumferences. 

In  this  figure  and  in  those  succeeding  it,  positive  hoop 
tensions  are  represented  by  ordinates  laid  off  above  the  line 
representing  the  trace  of  the  axial  plane  of  least  resistance, 
and  negative  hoop  tensions  (compressions)  are  laid  off  below 
this  line.     See  figures  5  and  6. 

RESISTANCE   OF    THE   CYLINDER., 

Bursting  Effort. 

Imagine  the  radial  pressure  on  a  unit  of  area,  or  /oj  to  be 
decomposed  into  two  components/'  and/^  figure  3,  respect- 
ively perpendicular  and  parallel  to  the  axial  plane,  O  R\ 
along  which  rupture  tends  to  occur;  and  consider  but  one 
quadrant  of  the  bore  at  a  time. 

Let  cp  be  the  variable  angle  made  by  the  radial  pressure 
with  the  plane  O  R', 

Then,  /'  =/o  sin  ^, 

and,  since, 

d Z'=-  R  d  cp^ 
J)' dZ=p(iR  sm  cpdcp  = —p^Rd  cos  cp. 

n  R 

Integrating  between  Z—^  and  Z=— -—   and    the    corre- 

<) 

spending  values  of  cp^  viz.  0  and  90°,  and  calling  P^  the 
total  pressure  on  the  inner  surface  of  the  quadrant  perpen- 
dicular to  the  plane  of  rupture,  we  have 


=/ 


0 


XIX. — GUN    CONSTRUCTION. 


And  for  the  force  acting  on  both  quadrants  to  lift  the  semi- 
cylinder  from  the  axial  plane,  or  for  the  bw'sting  effort 

%F=p,%R.  (2) 

This  might  have  been  inferred  from  the  fact  that  the  burst- 
ing effort  is  independent  of  the  configuration  of  the  surface, 
upon  which  it  acts. 
Eesistance. 

The  bursting  effort  must  be  in  equilibrium  with  the  sum 
of  the  tangential  stresses  developed  in  both  quadrants,  or 
in  figure  2. 

27'=/o2i?  =  2^/=2  X  areaierr'J?' 

or 


A=2--^-.  (3) 


COROLLARIES.  I 

1.  The  maximum  permissible  value  of  T\s  the  elastic  limit 
of  the  material  under  tensile  stress.  Calling  this  0  and  repre- 
senting by/g  the  corresponding  powder  pressure  we  have 

}.=e^.  (4) 

Equation  (4)  gives  the  means  of  determining  the  maximum 
pressure  for  a  gun  of  which  the  corresponding  section  is 
known,  or  of  determining  the  thickness  of  which  a  gun  of  a 
given  caliber  should  be  made  to  resist  a  given  pressure. 

2.  If  guns  be  similarly  proportioned,  R'  •=znR^  whence 
by  substitution 

/o=^^-  (5) 


X13t.— CUJ^  C0N§TRt)Ctl6N. 


Equation  (5)  shows  that  all  similar  guns  of  the  same  material 
can  resist  the  same  maximum  pressure. 

In  the  old  cast-iron  guns,  in  which  for  the  reinforce,  n  was 
generally  taken  equal  to  3,  or  the  walls  of  the  gun  made 
one  caliber  thick,  /o  =  f  ^j  i^  the  metal  be  without  internal 
strain.  Chapter  XV,  page  21. 

3.  Since  <  1,  A  <  6^  unless  i?  =  0  or  ^'  =  oo .     Or 

n 

the  powder  pressure  must  always  be  less  than  the  elastic 
limit  of  the  material. 

4.  The  curves  of  figure  4  are  constructed  from  equation  1, 
using  a  constant  value  of  ^'j=  6  and  taking  7"=  d  and 
«  =  3;  2;  f  respectively.  It  is  apparent  that  as  n  dimin- 
lishes  the  curve  T t;  T^t^;  T'  t'  becomes  more  nearly 
parallel  to  O R\  and  the  area  beneath  the  curve  tends  to 
increase  from  this  cause.  On  the  other  hand,  this  area  tends 
to  diminish  from  the  decrease  in  the  thickness  of  the  wall 
of  the  gun  in  consequence  of  the  increase  in  the  radius  of 
the  bore:  there  is  consequently  some  value  of  n  which  will 
make  this  area  a  maximum. 

To  determine  the  value  of  n  corresponding  to  a  maximum 
area  or  resistance  to  bursting,  denote  this  resistance  by  6", 
and  since  it  is  equal  to  the  maximum  bursting  effort  we  have 
from  equations  (2)  and  (4) 

Regarding  R'  as  constant  and  differentiating  we  have 


7    C 

Whence,  placing  — ^  =  0  we  find 

R'=  %R,        or        ;?  =  2. 


XlX. — GUN    CONSTRUCTION. 


That  is  to  say,  as  shown  by  the  following  table,  that  when 
R'  is  fixed,  if  the  thickness  of  the  wall  is  one-half  the  caliber, 
the  gun  can  withstand  a  greater  bursting  effort  than  with  any 
other  thickness. 

Table  for  R'  =  6. 
n=S         R=2         S'  =  ^d, 
n=2         R^S         S"  =  ^  d  =  i  S', 
«  =  f         R=  4:        S'"  =  id=  S\ 

It  is  to  be  noted  however,  that  since  the  bursting  effort  for 
one  quadrant,  or  R,  is  equal  to/„  Ry  if/„  be  kept  constant, 
-P  increases  with  R,  so  that,  under  ordinary  circumstances, 
the  thicker  is  the  wall  exposed  to  gas  pressure,  the  greater  by 
Equation  (4)  will  be  the  value  of /^. 

In  order,  as  R  increases,  to  diminish  the  value  of  the 
radial  stress,  we  may  form  the  gun  of  two  or  more  con- 
centric cylinders.  This  has  been  done  by  boring  out  old  cast- 
iron  guns  and  lining  them  with  a  tube;  since,  for  the  same 
bursting  effort,  the  pressure  per  unit  of  area  on  the  cast-iron 
is  diminished  because  the  area  pressed  is  increased.  This 
will  occur  even  if  the  material  of  the  tube  be  of  copper,  the 
resistance  of  which  may  be  neglected,  and  which  may  there- 
fore be  supposed  to  act  only  by  transmitting  the  pressure 
to  the  outside  walls. 

Within  limits  the  thicker  is  the  tube  and  the  greater  its 
value  of  jE,  the  stronger  will  be  the  composite  gun,  since 
for  a  given  stress  on  the  exterior  of  the  tube  the  less  will 
be  the  strain  on  the  adjacent  walls,  and,  therefore,  the 
smaller  will  be  the  maximum  stress  that  the  exterior  wall 
will  be  called  upon  to  bear.  Conversely  the  power  of  such 
guns  may  be  greatly  increased.     See  /i,  Chapter  XI,  p.  21. 

6.  From  the  preceding  corollary  it  follows  that  if  a  gun, 
the  dimensions  of  which  are  fixed,  be  composed  of  several 


XIX. — GUN   CONSTRUCTION. 


concentric  cylinders,  each  one  will  be  in  the  condition  of 
maximum  strength  if  its  internal  radius  is  half  its  external 
radius,  or  that  the  successive  radii  of  contact  will  be  in 
geometrical  progressio7i.  This,  which  is  known  as  Gadolin  s 
law^  is  sometimes  applied  in  modern  gun  construction. 


EQUALIZATION  OF  STRAINS. 

Preceding  considerations  show  that  owing  to  unequal 
distribution  of  the  strains  in  a  homogeneous  gun,  the 
strength  of  the  gun  increases  much  less  rapidly  than  the 
thickness  of  the  walls. 

The  most  favorable  case  would  be  when  the  whole  thick- 
ness of  the  wall  was  under  a  uniform  strain,  since  then  the 
maximum  pressure  would  be 

which  would  be  n  times  greater  than  that  given  by  equation 
(5).  This  result  can  be  approximated  to  only  by  the  sepa- 
rate or  combined  application  of  two  plans  commonly  known 
as  the  methods  of  Varying  Elasticity  and  of  Initial  Tension. 
These  are  actually  however,  but  variations  of  the  former 
principle. 

VARYING    ELASTICITY. 

This  consists  in  varying  the  elasticity  of  the  concentric 
cylinders  as  explained  in  Chap.  XV,  page  11.  The  elasticity 
may  be  measured  either  by  its  coefficient  or  by  its  limit. 
This  divides  the  subject  into  two  heads. 

1.  Varying  Coefficient,  or  Rate  E. 

Suppose  the  gun  to  be  composed  of  two  concentric  cylin- 
ders, the  tube  containing  the  bore,  and  the  jacket.  If  these 
are  of  the  same  material  the  stress  transmitted  to  the  jacket 


10  XTX. — GUN    CONSTRUCTION. 

will  follow  Barlow's  law.  But  if  the  jacket  be  made  of  a 
metal  with  E'  >  E,  then  the  stress  on  its  inner  surface  due 
to  the  strain  arising  from  a  given  increase  in  the  external 
diameter  of  the  tube  will  be  increased.  For  calling  e  the 
common  strain,  /,  /,  the  corresponding  stresses,  and  E^  E\ 
the  coefficients  of  elasticity  respectively  of  the  tube  and 
the  jacket. 

If  the  value  of  E  increase  as  r*,  then  the  stress  on  the  inner 
surface  of  the  wall  will  he  equal  to  that  on  the  inner  surface 
of  the  tube. 

For,  let  us  call  e^  the  strain  at  the  elastic  limit  of  the 
tube,  then 

8 
'^  =  ^ 
At  the  outside  of  the  tube  the  strain  will  be 

This  will  cause  a  stress  on  the  inner  wall  of  the  jacket 
E'e  J^         E'  jR^ 

If  now    E  :  E'  ::  F?  :  R'\    E'  R^  =  ER'^  and  t'=  d. 

The  thinner  is  the  outside  wall  the  less  will  the  stress 
vary  throughout  its  thickness,  so  passing  to  the  limit  we 
may  say —  That  to  develop  an  uniform  resistance  throughout  a 
cylinder  the  coefficients  of  elasticity  of  the  eleme7itary  concetitric 
cylifiders  must  vary  as  the  squares  of  their  radii. 

This  principle,  though  frequently  referred  to  in  gun  con- 
struction, is  now  of  little  practical  importance,  since  steel, 
the  coefficient  of  elasticity  of  which  is  constant,  and  is 


XIX. — GUN   CO^STRUCTION.  11 

greater  than  that  of  any  other  cannon  metal,  is  now  gen- 
erally employed  for  all  portions  of  the  gun. 

2.  Varying  Limit  of  Elasticity. 

Equation  (1)  shows  that  the  stress  on  any  cylinder  is 
always  greatest  on  its  inner  surface,  and  Equation  (4)  that 
for  a  given  gun  the  value  of  p^  is  limited  by  the  elastic  limit 
of  the  tube. 

Consequently,  if  the  value  of  ^is  constant,  we  may  in- 
crease the  strength  of  the  gun  by  increasing  the  elastic  limit 
of  the  tube. 

This  may  be  done  in  three  ways. 

a.  By  increasing  the  pt'ifuitive  elastic  limit  hy  varying  the 
composition  or  structure  of  the  tube.  This  is  not  practically 
done. 

b.  By  giving  it  a  special  elastic  litnit  before  the  bore  is  finished, 
viz.  :  1st;  by  raising  the  elastic  limit  itself  by  preliminary  ten- 
sion, as  by  mandrehng  (Chap.  XV,  p.  22),  or  .by  firing  high 
proof  charges.  2nd  ;  by  lowering  the  origin  of  stresses  by  a 
preliminary  compression,  as  by  temporarily  wrapping  the  tube 
with  successive  layers  of  wire  until  the  surface  of  the  bore 
receives  a  permanent  set. 

c.  The  principle  of  initial  tension  consists  in  subjecting  the 
interior  cylinders  to  a  stress  of  compression  by  the  reciprocal 
extension  of  the  outer  cylinders. 

The  effect  is  to  increase  the  work  required  to  deform  the 
inner  cylinders,  in  which  the  strains  due  to  firing  are  the 
greatest,  by  diminishing  the  work  required  to  deform  the 
outer  cylinders,  in  which  the  strains  due  to  firing  are  the 
least. 

The  foregoing  explains  the  gain  in  strength  by  mandrel- 
ing,  and  also"  why  the  heat  of  firing  may  really  tend  to 
strengthen  a  gun  instead  of  to  weaken  it  as  is  generally 


VZ  XIX. — GUN   CONSTRUCTION. 

supposed;  since  in  both  cases,  the  inner  concentric  cylinders 
being  expanded  more  than  those  exterior  to  them,  stresses 
are  developed  in  the  exterior  cylinders  which  resist  the  further 
extension  of  the  inner  portions. 

It  also  explains  the  advantage  of  forming  the  tubes  of  more 
ductile  material  than  the  jacket  and  hoops,  since  if  excessive 
powder  pressure  should  expand  the  bore  beyond  its  elastic 
limit,  the  initial  tension  developed  outside  would  tend  to 
prevent  its  further  dilatation. 

It  accounts  for  the  former  preference  for  bronze,  the  duc- 
tility of  which  sometimes  caused  such  guns  to  fissure  first 
on  the  outside,  where  it  was  unsupported,  while,  on  the 
contrary,  cast-iron  would  crack  first  on  the  surface  of  the 
bore  where  the  danger  would  less  readily  be  seen. 

Rodman's  process  of  cooling  cast-iron  guns  from  the  in- 
terior by  a  stream  of  water,  while  the  exterior  of  the  flask 
was  heated  by  fires,  was  intended  to  utilize  this  principle 
and  was  the  first  instance  of  its  application  on  a  large  scale. 
(Chap.  XV,  p.  21.) 

But,  while  the  cooling  of  the  exterior  portions  of  the  cast- 
ing might  be  retarded  relatively  to  that  of  the  portions  next 
to  the  bore,  it  could  not  be  postponed  until  all  the  interior 
portions  had  solidified. 

Consequently  the  state  of  rest  of  such  a  gun  could  be 
represented  by  figure  5  in  which  the  dotted  lines  represent 
what  was  desired  and  the  full  line  what  was  attained.  The 
process  was  besides  uncertain,  since  guns  have  been  known 
to  break  spontaneously  from  internal  stresses  so  developed. 

I  APPLICATION  TO  BUILT  UP  GUNS. 

The  results  sought  by  Rodman  may  be  attained  much 
more  certainly  by  the  process  of  building  up  guns  as  ex- 
plained in  Chapter  XV.    In  such  a  gun  if  the  tube  be  com- 


XIX. — GUN   CONSTRUCTION.  13 

pressed  until,  under  the  law  by  which  the  stresses  vary,  the 
elastic  limit  of  compression,  p,  be  reached  on  the  surface 
of  the  bore,  then  the  effective  value  of  the  maximum  tan- 
gential stress  to  which  this  surface  may  be  safely  exposed 
on  firing  will  be  6  -\-  p  and  the  maximum  safe  pressure  for 
the  tube  will  approach  as  a  limit 

J.  =  iS  +  p)'^. 

The  effect  of  this  pressure  is  shown  in  figure  6,  in  which 
the  stress  will  change  from  —  p  to  4-  ^  on  the  surface  of 
the  bore.  If  we  take  p=  6,  as  is  commonly  done,  then  the 
stress  on  the  exterior  of  the  tube  will  change  from  — ^'  7\ 
to  -^jR^  T^  as  shown. 

Now  consider  the  jacket.  The  negative  tension  of  the 
tube  is  due  to  a  positive  tension  of  the  jacket  resulting  from 
shrinkage.  Since  the  system  is  in  equilibrium,  the  algebraic 
sum  of  the  tensions  on  the  tube  and  the  jacket  must  be  equal 
to  0;  and,  since  from  Barlow's  law  the  tension,  whether 
positive  or  negative,  is  always  numerically  greatest  on  the 
inner  surface  of  a  cylinder,  we  would  have  the  condition 
represented  by  figure  6,  in  which  the  area 

RpT^R'  =  area  R'  T'  T"  R" . 

This  represents  the  state  of  the  system  at  rest. 

It  is  evident  that  the  configuration  of  the  stress  area 
on  the  jacket,  and  therefore  the  maximum  stress,  R'  T\ 
which  it  is  called  on  to  sustain  from  the  shrinkage,  will 
depend  upon  the  thickness  of  the  jacket.  Also  that  R'  T' 
must  not  only  not  exceed  the  elastic  limit  under  tension,  6' ^ 
of  the  jacket,  but  must  be  so  far  beneath  it  as  to  admit  of 
•the  increment  due  to  firing. 

Now  suppose  the  system  to  be  placed  in  action  by  the 
powder  pressure  and  for  simplicity  assume  that  pz=:  0  =.6', 


14  XIX. — GUN    CONSTRUCTION. 

As  the  tension  on  the  surface  of  the  bore  changes  from 
—  pto  -\-  6  the  strain  on  the  surfaces  of  contact  will  increase 
the  tension  there  by  a  quantity. 

For  the  tube  this  will  simply  change  the  sign  of  the  stress 
from  —  to  +. 

For  the  jacket  the  addition  will  be  positive,  the  most 
favorable  case  being  when  the  dimensions  of  the  jacket  are 
so  chosen,  as  in  figure  6,  that  the  tension  at  rest  +  the 
tension  in  action  =  6'.  The  state  of  the  system  in  action 
is  shown  by  the  dotted  lines  of  figure  6. 

The  tangential  resistance  of  the  system  will  be  propor- 
tional to  the  sum  of  the  areas  p  R  B  T^  R'  T^  p  {=%s) 
+  R'  T/  T,^  R"  R'  {=  s')  -  R'  T'  T"  R"  R'  (=  s;)    or 

:2 

:2  =  2^  +  /-^,  and/o=   ^• 

The  dimensions  of  figure  6  render  such  a  gun  about  twice 
as  strong  as  if  it  were  a  simple  tube  of  the  same  size  and 
elasticity. 

It  is  evident,  that  if,  as  on  page  9,  we  suppose  the  gun 
to  consist  of  an  indefinite  number  of  cylinders  in  which  the 
initial  tensions  are  properly  applied,  the  thinner  the  cylinders 
are  made,  the  less  will  be  the  difference  of  the  tensions  on 
their  interior  and  exterior  surfaces  and  the  more  nearly  will 
the  broken  line  d  T,  T/  r,,  become  parallel  to  O  R" ,  or 
the  more  nearly  will  the  resistance  of  the  gun  approach  the 
ideal  case. 

The  difficulties  of  manufacture  have  generally  limited  the 
number  of  cylinders  to  less  than  5  but  these  difficulties  can 
be  overcome  by  making  the  cylinders  of  continous  wire 
wrapped  around  a  central  tube. 


XIX. — GUN  CONSTRUCTION.  15 


SHRINKAGE. 

It  is  seen  that  the  initial  tension  depends  primarily  on 
the  shrinkage.  In  built  up  guns  this  may  be  due  to  heat- 
ing the  exterior  cylinder  as  described  in  Chap.  XV,  or  to 
forcing  by  hydraulic  pressure  one  cylinder  within  another, 
the  contact  surfaces  being  reciprocally  conical,  or  by  wind- 
ing wire  continuously  over  a  central  tube.  By  whatever 
method  the  result  may  be  attained,  the  stress  on  the  contact 
surfaces  is  due  to  the  strain  resulting  from  the  compression 
of  the  inner  cylinder  and  the  extension  of  the  exterior. 

To  determine  the  shrinkage  required  to  produce  a  given 
initial  compression  without  exceeding  either  p  in  the  inner 
cylinders  when  the  system  is  at  rest  or  6  in  the  exterior 
when  the  system  is  in  action,  is  one  of  the  principal  objects 
of  the  different  theories  of  gun  construction  now  in  vogue. 
A  full  discussion  of  these  theories  is  not  possible  in  this 
course,  but  the  following  treatment  of  the  subject  based 
upon  Barlow's  law  illustrates  the  methods  now  employed. 

Let  e,  e'  be  the  strains  on  the  adjacent  surfaces  of  the 
tube  and  jacket,  for  the  corresponding  stresses  R'  T^  =  /, 
and  R'  T'  ==  /'  and  let  o*  =  <?  +  <?'  be  the  shrinkage  strain. 

/  t' 

Then  since    e—  —=^   and    e'  =  -=r  ,  from  note,  page  21, 
jb  JtL 

<T=-^  =  ^{t+n  or  AJi'=  5  c+o- 

Consequently,  as  stated  in  Chapter  XV,  the  tube  would 
be  turned  to  a  diameter 

2R' 


(/  +  0  +2^' 

and  the  jacket  would  be  bored  to  its  finished  size.     The 
effect  of  shrinkage  would  be  to  vary  the  radii  somewhat  from 


16  .  XIX. — GUN   CONSTRUCTION. 

those  assumed,  and  to  increase  the  length  of  the  tube. 
These  variations,  which,  for  this  discussion  are  not  taken 
into  account,  afford  one  of  the  best  means  of  testing  the 
accuracy  of  the  hypotheses  upon  which  different  theories  of 
gun  construction  are  based. 

LONGITUDINAL  STRESS. 

This  tends  to  "unbreech"  a  gun  or  to  produce  what  is 
known  as  a  "ring  fracture,"  the  plane  of  which  approaches 
that  of  a  right  section. 

In  homogeneous  guns  it  was  sufficiently  resisted  by  the 
sections  required  to  resist  the  tangential  stress;  but,  in  com- 
posite b.  1.  guns,  except  so  far  as  friction  due  to  shrinkage 
and  powder  pressure  may  assist,  that  portion  which  contains 
the  breech  block  has  to  support  this  stress  independently  of 
the  portions  which  give  tangential  strength. 

The  bursting  effort  is  tt  jR."^  p^.  It  tends  to  pull  the  piece 
apart,  generally  in  rear  of  the  trunnions  to  which  it  trans- 
mits the  pressure  causing  recoil.  Consequently  the  piece 
carrying  the  breech  block  must  be  firmly  united  to  the 
trunnions.  When  b.  1,  guns  were  first  made  the  block  was 
secured  to  the  tube,  but  this  arrangement,  although  theo- 
retically advantageous,*  is  no  longer  generally  employed.  It 
is  thought  that  the  radial  expansion  of  the  tube  diminishes 
the  bearing  of  the  screw  threads  of  the  breech  block,  and 
that  the  tube  is  inclined  to  fissure  through  the  screw  threads. 

Supposing  the  longitudinal  stress  to  vary  through  the 
cross-section,  its  resistance  may  be  determined  as  follows : 

*  From  the  analysis  referred  to  on  page  2,  it  follows  that  the  longitu- 
dinal stress  of  the  tube  should  develop  a  negative  radial  stress  which 
would  neutralize  a  portion  of  the  powder  pressure.  This  has  been  con- 
firmed by  experiment  on  a  small  scale,  and  it  is  said  that  recent  cannon 
made  abroad  have  the  block  screwed  into  the  tube. 


XIX. — GtJN  CONSTRUCTIOK.  17 


The  area  of  cross-section  of  an  elementary  cylinder  whose 
radius  is  r  and  the  thickness  of  which  is  dr  will  be  ^Ttrdr. 
This  will  receive  a  variable  stress  q  the  intensity  of  which 
will  vary  with  its  distance  from  the  axis,  so  that  the  resistance 
of  the  section  whose  internal  and  external  radii  are  i?"and  R' 

q%7trdr. 
n 

If  we  suppose  q  to  vary  by  Barlow's  law,  we  have 

Substituting  this  value  of  q  and  integrating  we  have  for 
the  total  resistance 

^  J!L=27rie^^Nap.log— . 

Equating  this  with  the  bursting  effort,  we  have  for  the 
condition  of  equilibrium 

A  =  2  0  Nap.  log  ^.  (6) 

In  modern  guns  the  ordinary  values  of  0,  R'  and  R  are 
such  that  the  maximum  value  of /^  allowed  by  this  equation 
is  considerably  greater  than  that  allowed  by  their  tangential 
resistance,  so  that  these  guns  are  abundantly  strong  against 
longitudinal  stress. 

Equation  (6)  is  useful  for  computing  the  pressures 
necessary  to  burst  spherical  shell  for  which  purpose  it  gives 
results  closely  confirmed  by  practice.  In  such  cases  for  B 
should  be  substituted  the  tenacity  of  the  material.  This  is 
allowable  since  the  ductility  of  such  castings  is  small. 

WIRE-WOUND  GUNS. 

The  peculiar  properties  of  cold  drawn  wire  described  in 
Chapter  XV;  the  direction  assumed  by  the  fibers  in  the 
gun,  and  the  increased  facility  of  construction  have  for 


18  $Ct5t. — GtJN  CONSTkUCtlOl^. 

many  years  made  this  material  a  favorite  subject  of  study 
by  gun  makers. 

Until  recently,  however,  the  difficulty  of  providing  suffi- 
cient longitudinal  strength,  and  mechanical  difficulties  con- 
nected with  the  attachment  of  the  ends  of  the  wires  have 
caused  steel  forgings  to  be  preferred. 

The  following  may  be  named  as  devices  intended  to  pro- 
vide the  longitudinal  resistance. 

Dr.  Woodbridge,  of  New  Jersey,  the  originator  of  the 
idea,  proposed,  after  winding  his  tube  to  immerse  the  entire 
gun  in  a  bath  of  melted  bronze,  so  as  to  braze  or  solder  the 
spirals  and  the  layers  together.  This  was  found  mechanic- 
ally impracticable  and  the  bath,  by  annealing  the  wire, 
de&troyed  much  of  its  elasticity.  Various  experimenters 
have  tried  longitudinal  bars  or  staves  connecting  the  trun- 
nions with  the  breech,  but  so  far  as  tried  these  are  not 
believed  to  have  given  satisfaction;  the  objection  appearing 
to  consist  in  the  difficulty  of  making  all  the  bars  resist 
equally,  for  otherwise  they  will  tend  to  rupture  in  detail. 
Crozier's  Wire  Wound  Gun. 

This  gun,  now  under  construction,  is  devised  by  Lieut. 
Crozier  of  the  Ordnance  Department. 

It  consists — 

1.  Of  a  thin  steel  tube  forming  a  core  for  the  winding; 
to  contain  the  rifling  and  to  prevent  the  erosion  of  the  wire. 
It  also  incidentally  gives  longitudinal  stiffness. 

2.  Of  wire,  to  give  tangential  strength.  This  is  preferably 
of  rectangular  cross-section.  Relying  upon  the  support  of  the 
wire  wrapping,  it  is  intended  to  produce  an  initial  preliminary 
compression  considerably  in  excess  of  p.  See  page  11.  For 
experimental  purposes  it  is  assumed  that  the  relatively  thin 
tube  will  withstand  dilatation  and  contraction  through  a 
considerably  greater  range  than  6  -\-  p. 


XIX. —  GUN    CONSTRUCTION.  19 

The  difficulties  in  attaching  the  wires  have  been  success- 
fully overcome  by  electro-welding.  According  to  the  method 
proposed  by  Mr.  Longridge  of  England  each  coil  of  wire  is 
wrapped  with  a  tension  diminishing  from  within  outwards,  so 
that  the  tension  of  the  inner  layers  will  be  eventually  less 
diminished  than  if  the  tension  of  winding  were  constant. 

In  such  a  gun,  properly  constructed,  the  tangential  strain 
developed  by  firing  will  be  uniform  throughout  the  entire 
thickness  of  the  walls. 

3.  Of  a  steel  cast  jacket  carrying  the  breech  block  at  one 
end  and  the  trunnions  at  the  other  and  so  furnishing  the 
required  longitudinal  strength.  It  also  gives  longitudinal 
stiffness  and  being  lightly  shrunk  on  it  also  affords  some 
tangential  resistance.  This,  the  heaviest  unit  of  construc- 
tion is  made,  of  cast  steel  on  account  of  its  cheapness,  its 
radial  distance  and  its  adaptability  to  the  present  state  of 
the  arts  in  the  United  States. 

Practical  Corrections. 

WEIGHT   OF   CANNON. 

The  dimensiojis  of  cannon  are  sometimes  increased  be- 
yond what  is  required  by  their  elastic  strength  so  as  to  in- 
crease their  weight  and  thereby  diminish  the  destructive 
energy  of  their  recoil;  because,  calling  E  this  energy,  and 
e  that  of  the  projectile  at  the  muzzle,  and  the  corresponding 
masses  and  velocities  respectively  J/,  ;//,  ?^and  v^  we  have 
from  the  equation  of  momenta,  the  general  equation, 

8      a  m 

M  V  =^  mv  or    MV=^mv     or   E^-^r-pe.       (7) 

M  ^  ^ 

Equation  (7)  is  an  important  one  to  remember,  particu- 
larly for  small  arms. 


20  XIX. — GUN    CONSTRUCTION. 

This  equation  is  not  exact,  since  it  neglects  the  momentum 
of  the  powder  gases,  (Chapter  XI,  page  18),  but  it  is  con- 
venient for  general  discussions.  For  a  more  exact  formula 
see  Chapter  XXII. 

LINERS. 

In  order  to  provide  against  the  erosion  of  the  bore,  large 
built  up  cannon  are  sometimes  lined  for  a  short  distance  in 
ifront  of  the  chamber  with  a  thin  tube  which  can  be  replaced 
with  comparative  facility.  Guns  which  are  properly  de- 
signed appear  more  likely  to  fail  from  this  cause  than  as 
the  result  of  stress. 

LIMITS. 

It  is  not  considered  advisable  to  work  up  to  the  limits  p 
and  6  as,  for  the  sake  of  illustration,  has  been  supposed. 
A  safe  margin  is  allowed  in  both  cases.  Indeed  the  inverse 
method  is  that  generally  followed,  the  gun  being  designed 
to  safely  resist  a  certain  value  of  /<,. 

It  can  be  shown  theoretically  that  no  great  advantage  is 
gained  as  to  tangential  strength  by  increasing  the  thickness 
of  the  walls  over  the  powder  chamber,  much  beyond  one 
caliber.     See  General  Remarks^  Appendix. 

gadolin's  law. 

Owing  to  the  practical  difficulty  of  making  perfect  forgings 
of  the  thickness  which  this  law  would  require  for  the  exterior 
layers  it  is  not  generally  observed. 


XTX. — GUN    CONSTRUCTION.  21 


Note  1,  Page  15. 


Let  R^  be  the  exterior  radius  of  the  tube,  and  R^  the  interior  radius  of 
the  jacket  before  shrinkage ;  and  let  R/  be  their  common  radius  after 
shrinkage. 

The  effect  of  the  shrinkage  will  be  to  diminish  the  radius  of  the  tube 

Similarly,  for  the  jacket  e'  =  •  ^      '-^  e,  since  /  <;  /''. 

The  total  shrinkage  will  be 

R^-R/       R/-R, 

R^  and  R^  are  so  nearly  equal  to  each  other,  and  so  large  when  compared 
with  the  numerators  of  the  fractions  that  either  R'  or  R^  may  be  used 
as  a  common  denominator  without  material  error.  R'  it  taken  because  it 
pertains  to  the  tube  on  which  the  excess  is  left  as  described  in  Chapter  XV, 
The  true  shrinkage  will  therefore  be  slightly  greater  than 


22  XIX. GUN  CONSTRUCTION. 


THE  ELASTIC  STRENGTH  OF  GUNS. 

By  Captain  L.  L.  Bkuff,  U.  S.  Ordnance  Department. 
The  object  of  this  discussion  is  to  give  a  general  idea  of 
the  methods  employed  in  modern  gun  construction,  for 
determining  the  strength  of  guns,  the  strains  to  which  they 
may  be  safely  subjected,  and  the  methods  by  which  the  re- 
quisite strength  may  be  obtained. 

Definitions. 

The  elastic  limit  of  a  metal  is  the  greatest  load  in  lbs.  per 
square  inch  of  section  which  the  metal  will  sustain  before  it 
acquires  a  permanent  set. 

There  are  various  elastic  limits,  such  as  those  for  tension, 
compression,  torsion,  etc.,  depending  on  the  manner  in  which 
the  stress  is  applied  but  the  only  ones  of  practical  importance 
in  gun  construction  are  those  for  tension  and  compression. 

The  modulus  of  elasticity  of  a  metal  (see  Michie's  Mechanics, 
art.  22),  is  the  ratio  of  the  load  or  stress  in  pounds  per  square 
inch,  to  the  elongation  or  strain  per  linear  inch  produced  by 
this  load  within  the  elastic  limit.  It  is  expressed  by  dividing 
the  stress  by  the  strain.  Since  within  the  elastic  limit  the 
strain  or  elongation  is  proportional  to  the  stress  or  load,  it  is 
evident  that  this  ratio  is  constant  for  the  same  metal.  Its 
value  for  all  gun  steel  is  taken  at  30,000,000  lbs. 

As  in  the  case  of  the  elastic  hmit,  there  are  various  moduli 
of  elasticity,  as  for  tension,  compression,  etc.,  but  those  for 
tension  and  compression,  which  are  the  only  ones  used,  agree 
so  nearly,  that  the  uniform  value  given  above  is  assumed  for 
both. 

Hooke's  Law. —  This  law  is  expressed  above.  It  is  as 
follows  :  Within  the  elastic  hmit  of  a  metal,  the  stress  is  pro- 
portional to  the  strain. 

Stress  and  Strain. —  In  the  discussion  stress  will  be  used  to 
denote  the  force  in  pounds  per  square  inch  producing  a  given 


^13^. — GUN   CONSTRUCTION.  2^ 


extension  or  compression  per  linear  inch,  and  strain  the  corres- 
ponding elongation  or  compression  produced  by  the  stress. 

General  Principles. 

The  construction  of  the  modern  gun  is  supposed  to  be 
understood.  That  is,  that  it  is  composed  of  an  interior  tube, 
surrounded  by  a  jacket  and  one  or  more  rows  of  hoops. 
That  the  jacket  carries  the  breech-closing  device,  and  that 
the  jacket  and  hoops  have  interior  diameters  which  are  less  than 
the  exterior  diameters  of  the  parts  they  envelop,  by  a  certain 
prescribed  amount,  and  that  the  difference  in  diameter  between 
the  enveloping  cylinder  and  the  enveloped  cylinder  is  called 
the  shrinkage.  In  order  to  place  the  smaller  or  enveloping 
cylinders  over  the  enveloped  cylinders,  the  former  are  ex- 
panded by  heat  till  they  will  pass  over  the  corresponding  sur- 
faces, when  they  are  cooled  in  place  by  the  application  of 
water. 

Theory. 

The  principle  of  initial  tension  is  employed  in  the  modern 
built  up  gun.  The  interior  layers  which  are  under  the  greatest 
strain,  due  to  the  action  of  the  powder  gas,  are  compressed 
by  the  exterior  layers,  jacket  and  hoops.  When  the  pressure 
of  the  gas  acts  upon  these  interior  layers,  it  has  first  to  over- 
come this  initial  compression,  and  then  to  extend  or  compress 
these  layers  until  they  reach  their  elastic  limit  for  extension  or- 
compression,  before  the  maximum  resistance  of  the  gun  is 
reached.  The  exterior  layers  are  subjected  to  initial  tension, 
by  which  their  capacity  for  resisting  interior  pressure  is  partly 
diminished,  but  owing  to  the  law  of  its  transmission,  the  strain 
upon  them  is  so  much  less  per  square  inch  than  it  is  upon  the 
interior  layers  that  they  are  able  to  resist  it.  Thus  the  interior 
layers  are  relieved  of  a  portion  of  the  strain,  due  to  the  action 
of  the  powder  gas,  and  the  strain  transmitted  to  the  exterior 
layers,  by  the  modern  process  of  gun  construction. 


24  XlX. — GUN   CONSTRUCTION. 


The  best  condition  for  strength  in  a  gun  is  when  every 
layer  of  metal  in  its  cross  section  is  strained  equally  by  a  given 
stress  or  pressure. 

The  foundation  of  the  theory  of  the  built  up  gun  is 
this.  That  ifi  whatever  state  the  gun  may  be  considered^ 
whether  under  the  pressure  of  the  powder  gas,  or  free  from  it, 
7ione  of  the  fibers  of  any  cylinder  in  the  gim  shall  be  elongated 
or  contracted  beyond  the  elastic  lifnit  of  the  metal  of  that 
cylinder^  which  elastic  limit  is  determined  by  the  test  of  the 
metal  in  a  testing  machine. 

Two  states  or  conditions  of  the  gun  are  considered  in  this 
discussion ;  one,  called  "  the  system  in  action,"  which  means 
that  the  gun  is  subjected  to  the  maximum  interior  pressure 
which  it  can  support  with  safety,  and  the  other,  called  "  the 
system  at  rest,"  that  is,  when  the  gun  is  free  from  the  pressure 
of  the  powder  gas,  although  the  strains  due  to  the  shrinkages 
still  exist. 

Methods  of  Discussion. 

The  general  method  of  discussion  is : 

First.  To  assume  a  cube  of  metal  the  length  of  whose 
edges  is  unity,  and  which  is  supposed  to  be  perfectly  elastic 
up  to  a  given  limit ;  to  deduce  the  equations  of  equilibrium 
which  show  the  relations  between  the  forces  acting  upon  this 
cube  in  directions  at  right  angles  to  its  faces,  and  the  corres- 
ponding elongations  and  contractions  produced  by  them. 

Second.  To  transform  these  equations  so  that  they  will  apply 
to  the  elements  of  a  cylinder  of  metal ;  or  in  other  words,  to 
deduce  the  equations  which  give  the  relations  between  the 
stresses  at  different  points  throughout  the  right  section  of  a 
single  cylinder. 

Third.  To  pass  from  a  single  cyhnder  to  a  compound 
cylinder  composed  of  any  number  of  single  cylinders,  and  to 
deduce  for  the  latter  the  compressions  and  extensions  pro- 


XIX.— GUN   CONSTRUCTION.  25 

duced  by  given  pressures,  and  the  shrinkages  or  differences 
of  diameter  which  will  produce  given  compressions  and 
pressures. 

FIRST. —  EQUATIONS  OF  EQUILIBRIUM  FOR  A  CUBE  OF  METAL 
OF  CONSTANT  ELASTICITY  WHOSE  EDGES  ARE  EQUAL  TO 
UNITY. 

It  has  been  found  by  experiment,  that  when  a  cubical  elastic 
solid  is  acted  upon  by  a  given  force  of  extension  or  com- 
pression in  a  direction  perpendicular  to  two  of  its  opposite 
faces,  this  force  produces  an  extension  or  a  compression  of 
the  cube  in  the  direction  of  the  force,  of  a  given  amount,  and 
a  corresponding  compression  or  extension  in  the  two  direc- 
tions at  right  angles  to  the  given  force  equal  to  one-third 
the  first  extension  or  compression. 

The  force  is  supposed  to  be  within  the  elastic  Umit  of  the 
solid. 

For  example,  suppose  a  force  of  extension  /*,  Fig.  7,  to  act 
upon  the  opposite  faces  of  a  cube  of  metal,  whose  edges  are 
each  one  inch  long.  If  it  extends  the  edges  a  a  a  ^^  of  a.n 
inch  it  will  shorten  the  edges  d  I?  d  and  c  c  c  ^  of  ^^  :=:  ^  oi 
an  inch,  and  the  same  for  any  other  force. 

In  figure  8 
Let  B  =  the  modulus  of  elasticity  of  the  cube. 

X,  V  and  Z=  three  forces  acting  at  right  angles  to  the 

faces  of  the  cube,  being  tensions  in  the  figure. 
X;  fi;  V,  =z  the  extensions  produced  by  the  three  forces 
Xy  Fand  Z,  respectively. 

Then  the  force  X,  according  to  the  preceding  principle, 
produces  an  elongation  in  its  own  direction  equal  to 

But  the  force  K  diminishes  this  elongation  by  the  amount 

iZ 


26  XIX — GUN    CONSTRUCTION. 

and  the  force  Z  by  the  amount 

Hence  the  total  elongation  in  the  direction  of  X  is 

In  the  same  way  we  have  for  the  total  elongations  in  the 
directions  of  Kand  Z 


'=4{-f-^) 


These  three  equations  express  the  relations  between  the 
elongations  of  the  faces  of  an  elastic  cube  whose  edges  are 
unity,  and  the  corresponding  forces  acting  on  them. 

SECOND. APPLICATION    TO    AN    ELASTIC    CYLINDER. 

We  have  supposed  the  three  forces  to  be  tensions.  In  the 
case  of  a  gun  cylinder,  however^  two  of  the  forces  are  ten- 
sions, one  acting  in  the  direction  of  a  tangent  to  the  cylinder, 
and  the  other  parallel  to  the  axis,  while  the  third  is  a  pressure 
and  acts  in  the  direction  of  the  radius.  In  Figure  9,  let  /  = 
the  radial  pressure,  /  =  the  tangential  tension,  ^  the  longitu- 
dinal tension,  per  unit  of  area. 

Substitute  /  for  X,  — J>  for  Y  since  it  acts  opposite  to  F, 
and  ^  for  Z,  and  the  above  equations  become 


} 


'--M'  +  T  +  l))  W 


XIX. — GUN    CONSTRUCTION.  27 

The  first  of  these  equations  expresses  the  total  change  per 
unit  of  length  in  the  direction  of  the  tangent  of  the  cyhnder  ; 
the  second  the  total  compression  (being  negative)  in  the 
direction  of  the  radius ;  and  the  third  the  total  change  in  the 
direction  of  the  axis,  due  to  the  three  forces  /,  /  and  q. 

In  order  to  apply  these  equations  in  practice  the  changes  of 
dimensions  must  be  expressed  in  terms  of  the  radii  of  the 
cylinder  and  of  the  forces  acting  upon  it.  To  express  the 
equations  in  these  terms  we  proceed  as  follows : 

Equations  of  Equilibrium   in   Terms  of  the  Radii  of  the 
Cylinder. 

Let  Figure  10  represent  a  section  of  the  cylinder  perpen- 
dicular to  the  axis. 
Let  R  =  interior  radius. 
R '  n:  exterior  radius. 
r  =  the  radius  of  any  circle  of  the  section. 
r'  =  any  other  radius  exterior  to  r. 
p  zzzthe  radial  pressure  per  unit  of  surface  at  the  distance 

r  from  the  axis. 
tz=.  the  tangential  stress  per  unit  of  surface  at  r, 
q  =  the  stress  per  unit  of  section  parallel  to  the  axis  of 
the  cylinder,  and  supposed  uniform  throughout  the 
section. 
/*=the    interior   radial   pressure   per    unit  of  surface, 

being  the  value  of  /  for  R. 
^'^the   exterior   radial   pressure  per  unit  of  surface, 

being  the  value  of  /  for  R' . 
T  and  T'  =  the  values  of  /  for  r  =  Rj  and  r=  i?'  re- 
spectively. 
^=the  modulus  of  elasticity. 
The  pressure/,  whether  acting  inward  or  outward,  develops 
in  the  direction  perpendicular  to  A  B,  Figure  10,  a  force 
equal  to  2j>r. 


28  XIX. — GUN   CONSTRUCTION. 

Increase  r  to  r',  and  represent  by  f  the  new  value  of/. 
This  develops  a  force  in  the  direction  perpendicular  \.q  A  B 
equal  to  2  p'  r* .  The  algebraic  difference  between  these  forces 
is  in  equilibrio  with  the  product  of  twice  the  thickness  of  the 
ring  r*  — ;'  into  the  mean  stress  throughout  the  ring,  which 
represent  by  r.     Hence 

2/  /  _  2  /r  =  —  2  T  (^  —  r) 

dividing 

P'r'  —pr  _        ^ 
r*  —  r 

passing  to  the  limit  of  the  ratio  in  the  first  member  by  making 

d{pf) 


(p'  r'  —pr\ 


limit  of  1 ,  ^ 

r'  ^ 


limit  of 

\> 
Hence 

d  (pr)  __ 


Taking  the  last  of  Equations  (8),  which  expresses  the  strain 
in  the  direction  of  the  axis  of  the  cylinder,  and  supposing 
this  uniform  throughout  the  cross-section,  we  have 

P\ 


^=M' 


i+8 


From  this  we  have 


or  t—  p=^^{q—  V  E)  (10) 

But  the  second  member  of  this  last  equation  is  constant, 
since  we  have  supposed  v  uniform  throughout  the  section ; 
hence 

/ — /  =  constant. 


XIX. GUN    CONSTRUCTION.  29 

From  which  we  may  unite 

t—p=  T—P (A) 

t—p=T'  —  F' (V) 

From  Equation  (10)  we  have 

t=P  +  i(q-vE)  (11) 

Substituting  this  for  /  in  Equation  (9)  we  have 

performing  the  differentiation  as  indicated ;  /  and  r  being 

variable, 

pdr  +  rdp  ^       o  /  Z7\ 

Jr         =  —  /  —  3(^— v^) 

reducing 

dr  dp 


r  ~~  2  /  +  3  (^  —  V  ^) 
Integrating 

log=  (y)  =  4  log.  (2/  H-  3  (?  -  V  ^  +  log.  C 

i-  =  ^(2/  +  3(?-r^)) 
Substituting  the  value  of/  +  3  (?  —  v  E)  from  (11)  we  have 

!  =  .(/+/) 

(/  -j-  /)  r'  =  —  =  constant 
From  which  we  can  write 

{t^-  p)r'  =  {T-^P)R' (Q 

{t-\-  p)r'  =  {T'  -\-P<)R''' {D) 

From   Equations   (A)  and   (B)  we  derive   the   following 
principle : 

The  difference  between  the  tension  and  the  'Pressure  is  the 
same  at  all  points. 


30  XIX. — GUN    CONSTRUCTION. 

From  (C)  and  {D)  we  have  the  following  principle : 

At  any  point  whatever^  the  sum  of  the  tension  in  the  direction 
of  the  circumference,  ajid  of  the  pressure  in  the  direction  of 
the  radius,  varies  inversely  as  the  square  of  the  radius. 

This  demonstration  is  given  by  Captain  Crozier,  Ordnance 
Department,  in  "  Notes  on  the  Construction  of  Ordnance," 
No.  35. 

Applications. —  It  has  been  shown  by  Captain  Birnie,  Ord- 
nance Department,  that  in  considering  the  radial  and  tangential 
strains  in  a  gun  cylinder,  we  may,  without  appreciable  error, 
omit  the  longitudinal  strain,  or  the  strain  parallel  to  the  axis, 
and  afterwards  consider  this  latter  strain  separately.  This 
conclusion  has  been  proved  to  be  correct,  by  actual  measure- 
ments of  guns  during  construction.  This  is  equivalent  to 
making  in  Equation  (8) 

q^o, 
when  the  equations  become 

In  the  last  equation,  which  gives  the  change  in  the  longi- 
tudinal direction,  this  change  will  be  produced  by/  and  /only. 
From  Equations  (C)  and  {D)  we  have 

(5-/  -j-  pi)  Ri  2  ^  (r-l.  p)  j^^ 

and  from  {A)  and  {B) 

T'  —  F'  =  T—F 
Combining  these  two  equations  and   ehminating   T'  we 

have 

■      F'^  +  J^         2  F' '  F' 
^  ^'  F'^  —  F*"  F"  —  F" 


/  = 


XI3^. — GUN   CONSTRUCTION.  31 

Substituting  this  value  in  (J)  and  (C),  combining  the  re- 
sulting equations,  and  eliminating/  we  have 

Ri^  —  R'         -I-         ^,2_^.  ^  (13) 

And  by  combining  and  eHminating  /  between  the  same 
equations  we  have. 

_      FJ^  —  P'  Ii'\.    J^'^^'iP—P')    1 

Substituting  these  values  of  /  and  /  in  Equations  (12)  we 
have 

2  {PR'  —  P'  R'^)      q^R'^  R'  i^P—  P')    1 
'^ ""    $(R"  —  R')jS    "f"    3{R''  —  R')£       r"    ^^^ 

_  ^(PR"—  P'  R'"")      4tR"  R'  {P—P')    1_ 
^—    d(R'^  —  R')£   ~"    S  {R' '  —  R')  E     r"     (^^^ 

_       ^{PR'  —  P'R'') 
^  —  ""    8  (i?"*  —  R')  E  vA ') 

These  equations  give  the  values  of  the  elongations  or  con- 
tractions in  terms  of  the  pressures  and  radii,  and  the  known 
modulus  E^  for  any  radius  r. 

Elastic  Strength  of  a  Simple  or  Single  Cylinder. 

Now  it  may  be  shown  that  the  greatest  elongations  and 
compressions  of  the  fibres  of  a  cyUnder  subjected  to  an  interior 
pressure  P,  and  an  exterior  pressure  P' ,  take  place  at  the  inner 
surface  of  the  cylinder.  (See  appendix,  Note  35,  on  the  Con- 
struction of  Ordnance.)  Assuming  this,  we  recur  now  to  the 
fundamental  principle  stated  above  "that  no  fibre  of  any 
cylinder  in  the  gun  shall  be  elongated  or  contracted  beyond 
the  elastic  limit  of  the  metal  of  that  cylinder." 

Let  Q  =  the  elastic  limit  for  tension, 

p  =  the  elastic  limit  for  compression  in  pounds  or  tons 
per  square  inch,  of  the  cylinder. 


82  XlX. — GUN   CONSTRUCTION. 


Then  the  extension  and  compression  at  the  elastic  Hmit  will 
be  respectively 

and  by  the  above  principle  these  must  be  equal  to  the  greatest 
values  of  /I  and  [z  respectively. 

Since  the  greatest  extensions  and  compressions  will  occur 
at  the  interior  of  the  cylinder,  we  have  for  their  greatest 
values  by  substituting  jR  for  r  in  (15)  and  (16) 


3  (i?' '  —  R')  E 


(18) 


f^  —  —  3  (i?' » —  R'YE  (^^) 

Placing  these  equal  to  -^  and  -^  respectively,  we  have 
.       (4:R"  +  2R')P—6R"  P' 


d(R''  —  R') 


I  2      pt 


___  (^R'^  —  2R')P—'2R'''P 
P—  3(R''  —  R') 

From  which  we  find  two  values  for  P,  viz.  : 
■^  4  i?'  ^  +  2  ^^ 

^     —  4:  R"  —  '2.R' 


(20) 


(21) 


Equation  (20)  gives  the  value  for  the  interior  pressure, 
which  will  cause  the  layer  of  metal  on  the  interior  of  the 
cylinder  to  reach  its  elastic  limit  by  extension,  and  Equation 
(21)  the  value  which  will  cause  the  same  layer  to  be  com- 
pressed to  its  elastic  limit ;  these  pressures  being  in  pounds 
or  tons  per  square  inch  according  as  d  and  p  are  expressed  in 
pounds  or  tons. 


XIX. — GUN   CONSTRUCTION.  83 

It  must  be  remembered  that  the  less  of  the  two  pressures, 
measures  the  elastic  strength  of  the  cyHnder. 

THIRD. —  THE  ELASTIC  STRENGTH  OF  A  COMPOUND  CYLINDER, 
OR  OF  A  BUILT-UP   GUN. 

For  the  sake  of  clearness  in  the  nomenclature,  and  of  sim- 
plicity in  discussion,  the  gun  will  be  supposed  to  consist  of  two 
cylinders  only,  shrunk  one  upon  the  other,  and  the  resistance 
of  this  compound  cylinder,  and  the  shrinkages  to  be  used  in 
its  construction,  will  be  deduced. 
In  figure  11  let 

P^  =  the  maximum  internal  pressure  to  which  the 

gun  can  be  subjected. 
P^  ■=.  the  normal  pressure  at  the  surface  of  contact 

of  the  two  cylinders. 
P^  •=.  the  exterior  normal  pressure. 

A'  Pv  P-i  ^^  variations  in  the  pressures,  P^^  P^  and  P^  due 

to  any  cause  whatever. 
The  above  pressures  and  variations  of  pressure  are  those 
which  exist  with  the  "  system  in  action,"  —  that  is  when  the 
maximum  gas  pressure  is  acting  on  the  bore. 
Let 

PI  =  the  normal  pressure  acting  at  the  surface  of 

contact  of  the  two  cylinders  when  the  system 

is  at  rest — that  is,  when  the  pressure  of  the 

gas  does  not  act  on  the  bore. 

//  =  the  variation  of  P^  due  to  any  cause  whatever. 

J?g,  i?j,  R^  =  the  radii  of  bore,  of  interior  of  second  cylinder, 

and  of  exterior  of  second  cylinder  respectively. 

0„,  0j  =:  elastic  limits  of  inner  and  outer  cylinders  for 

extension. 
p^,  pj  =  elastic  limit  of  same  for  compression. 
E^,  E^  =  moduli  of  elasticity  of  metal  of  cylinders. 


34  XIX. — GUN    CONSTRUCTION. 


Writing  Equations  (20)  and  (21)  we  have 

^    -  4^'^  +  2i?^~  ^^ 

^     —  4^'"  — 2i?^  ^^^ 

Now  it  will  be  remembered  that  in  the  case  of  a  single 
cylinder,  Equation  (20)  gives  the  value  of  Z*^^^,  the  interior 
pressure  which  will  cause  the  layer  of  metal  on  the  interior 
of  the  cylinder  to  reach  its  elastic  limit  by  extension,  and 
Equation  (21)  the  value  of  P^^  the  interior  pressure  which 
will  cause  the  same  layer  to  be  compressed  to  its  elastic  limit. 

Taking  the  outer  or  second  cylinder  of  the  gun,  it  is  always 
under  a  strain  of  extension  both  in  action  and  at  rest,  and 
hence  Equation  (21)  will  not  apply  to  it. 

Equation  (20)  must  therefore  be  used.  To  apply  it  to  the 
present  case,  R  and  R'  in  (20)  are  the  inner  and  outer  radii, 
which  now  become  R^  and  R^  respectively.  /*is  the  interior 
pressure,  and  it  now  becomes  P^,  P'  is  the  exterior  pressure, 
and  it  becomes  P^.  But  this  exterior  pressure  on  the  second 
cylinder  is  simply  that  due  to  the  atmosphere,  and  it  is  so 
small  in  comparison  with  the  other  pressures  considered  that 
it  may  be  neglected.     Hence 

P.  —  o. 

Also  Q  becomes  Q^.  Making  these  substitutions  in  (20)  we 
have 

_%{R^-R^)Q, 
'  ~  4:  Rl  +  2  R,' 

This  gives  the  value  of  the  interior  pressure  on  the  outer 
cylinder  which  will  cause  its  inner  layer  to  be  strained  to  the 
elastic  limit  for  tension,  and  as  this  value  is  expressed  in 


XIX. — GUN    CONSTRUCTION.  85 

known  terms,  P^  can  be  readily  calculated.     The  value  of  0^ 
is  obtained  from  test  of  the  metal  in  a  testing  machine. 

Now  taking  the  inner  cylinder,  the  pressure  P^  just  found,  acts 
not  only  on  the  interior  of  the  outer  cylinder,  but  also  on  the 
exterior  of  this  inner  cylinder.  Hence  one  of  the  normal 
pressures  acting  on  this  inner  cylinder  is  known,  and  we  have 
to  calculate  the  other.  • 

This  inner  cylinder  is  not  only  extended  by  the  action  of 
the  powder  gas,  but  it  is  also  compressed  radially  by  this 
pressure,  and  it  is  subjected  to  a  strain  of  compression  by  the 
force  P^  which  we  have  just  found.  In  other  words  the  inner 
cylinder  is  subjected  to  both  tension  and  compression,  and 
hence  it  is  necessary  to  calculate  both  strains,  and  to  take  the 
smaller  as  the  limit  of  its  elastic  resistance. 

Referring  to  Equations  (20)  and  (21)  the  following  changes 
must  be  made  to  apply  them  to  the  inner  cylinder  — 

P  becomes  P^ 

P'       "        P^ 

R        "        R, 

R'       '*        R^ 

e        -        6^ 

Making  these  substitutions  we  can  write 

,,     3{R,^-Rl)  e,+  6R,-'P, 
V  4:R,'  +  2  Rl 

»     ~  4:R,^  ^2Rl 

Substituting  in  these  equations  the  known  values  of  the 
radii,  and  of  ^^  and  p^  together  with  the  value  of  P,  just  cal- 
culated, we  obtain  two  values  for  /*„,  the  smaller  of  which  is 
the  limiting  value  of  the  pressure  for  the  compound  cylinder 
under  discussion. 


86  XIX. — GUN    CONSTRUCTION. 


For  convenience  of  reference  these  equations  are  collected 
here — 

p   ^  3  (i?i  -  R,' )  e, 

4  7?^  +  2  R,' 

^  (n  _  3(^.'-^a  K^^^.'P.  V  (22) 

•^o     ~  4i?,^  +  2J?,1  ^  ^     ^ 

3  {R,   -  i?^)  p„  +  2  i?,'  -P. 


p(2)    _ 


The  values  of  P,  obtained  from  Equations  (22),  are  the 
pressures  which  will  cause  the  interior  of  each  cylinder  to 
reach  its  elastic  limit  for  extension  or  compression;  and  since 
the  greatest  strains  in  a  cyHnder  occur  at  its  interior  surface, 
and  since  also  no  part  of  any  cylinder  must  be  strained  be- 
yond its  elastic  limit,  it  is  evident  that  the  values  of  P,  thus 
obtained,  represent  the  greatest  strains  to  which  the  cylinders 
can  be  subjected.  It  will  be  seen  hereafter,  that  these  values 
cannot  always  be  used  in  practice,  since  the  bore  in  the  state 
of  rest,  may  be  compressed  beyond  its  elastic  limit,  by  the  use 
of  these  values. 

It  is,  therefore,  necessary  now  to  consider 

The  System  at  Rest. 

Equations  (22)  give  the  pressures  acting  for  the  sys- 
tem when  under  the  maximum  pressure  of  the  powder 
gas.  It  is  evident,  however,  that  when  the  system  is  at 
rest,  great  pressures  will  exist  at  the  surface  of  contact  of 
the  two  cylinders,  due  to  the  shrinkage  of  one  on  the  other. 
These  pressures  generally  increase  from  the  exterior  to  the  in- 
terior, and  the  interior  of  the  bore  is  generally  compressed 
from  this  cause  to  a  greater  degree  than  any  other  part  of  the 
gun.  This  compression  of  the  bore  may  be  so  great  as  to 
exceed  the  elastic  limit  for  compression  of  the  metal  of  the 
inner  cyHnder,  and  thus,  although  the  gun  is  properly  calcu- 
lated for  action,  the  principle  upon  which  the  whole  structure 


XIX. — GUN   CONSTRUCTION.  37 

is  built  may  be  violated,  when  the  gas  pressure  is  removed. 
In  this  case",  the  elasticity  of  the  tube  is  destroyed., as  effect- 
ively as  if  by  the  powder  pressure. 

It  is  evident,  also,  that  when  the  powder  pressure  ceases, 
the  pressure  which  existed  at  the  surface  of  contact  of  the  two 
cyhnders  will  change,  and  will  assume  some  other  value  for 
the  state  of  rest.  The  value  of  this  variation  of  pressure  at 
the  surface  of  contact  has  been  denoted  by  /,  and  at  the  sur- 
face of  the  bore  by /o-  The  value  of  the  pressure  at  the  sur- 
face of  contact  for  the  state  of  rest  has  been  represented 
by  P\ 

Now  it  is  evident  that  the  difference  between  the  pressure 
in  action  and  at  rest  for  any  surface,  gives  the  variation  in  the 
pressure  at  that  surface.  Hence,  since  the  pressure  at  the  in- 
terior of  the  bore,  when  the  system  is  at  rest,  is  zero,  we  have 

and  also 

When  these  changes  of  pressure  occur,  they  are  accompanied 
by  corresponding  changes  of  dimensions  of  the  surfaces  at 
which  they  act,  and  these  changes  of  dimensions  depend 
directly  upon  the  variations  of  pressure.  The  greatest  changes 
of  dimensions  occur  in  the  direction  of  the  circumference  or 
of  the  tangent  to  the  surfaces,  and  Equation  (18)  gives  the 
value  of  these  changes  for  the  interior  surfaces. 

To  Calculate  these  Changes  of  Dimensions. 

The  variation  of  pressure  acting  on  the  outer  cylinder  .s 
/,,  and  the  exterior  pressure  is  zero,  being  that  of  tlie  atmos- 
phere.    Hence,  substituting  in  Equation  (18)  for  P  its  value 

p^  and  making 

/"  =  o 
R   -^  R, 
R'  ^  R, 
E  =^  E, 


38  XIX. — GUN    CONSTRUCTION. 


we  can  write 


^^(4^^  +  2i?r)A 


3  (J^l  —  R:^)  E, 

This  represents  the  change  of  dimensions  of  the  interior 
of  the  outer  cyUnder  per  unit  of  length  of  circumference, 
under  the  change  of  pressure  represented  by  p^. 

To  find  the  change  of  the  exterior  of  the  tube  due  to  the 
variations  of  pressures  p^  and  /,  which  act  on  it,  we  recur  to 
the  general  Equation  (15),  which  gives  the  change  in  the 
direction  of  the  circumference,  or  of  the  tangent,  of  any 
cylinder  whose  exterior  and  interior  radii  are  R'  and  R  at  the 
distance  r  from  the  axis.  Replacing  r  by  R'  since  the  change 
at  the  exterior  of  the  cyHnder  is  now  required,  we  have 

_  %R^P-{^R^  +  ^R'^)P' 
^  -  'i{R''^-R^)E  ^^^^ 

To  apply  this  to  the  inner  cylinder  now  under  discussion 
make 

R'    =    Ry 

and  we  write 

6  Rl  A.  -  (4  Rl  +  2  R,')  A  . 


A-= 


3  {R,^  -  Rf)  E, 


for  the  value  of  the  change  of  exterior  of  inner  cylinder  or 
tube. 

Now  since  the  outer  surface  of  the  tube,  and  the  inner 
surface  of  the  outer  cylinder  are  in  contact,  the  same  change 
of  dimensions  must  occur  in  both,  at  this  surface  of  contact, 
and  hence  the  two  values  of  X  obtained  above  are  equal. 


XIX. — GUN   CONSTRUCTION.  89 

We  have  therefore 

6  RIP,  —  (4  i?^  +  2  R^)p,       (4  i?l  +  2  R^)  /, 


/i  = 


Solving  this  equation  with  reference  to  p,  we  have 
QR,E,[Ri-R,']p^ 


E,  {R,—Rn  (4i^o  +  ^Rn  +  E,(J^,^  —  J^t)  (4^^  +  2  R,') 

(24) 
Now  in  this  equation /„  is  known,  since  it  is  equal  to  — P^ 
as  before   shown,  and  R^  has   been    already  calculated  by- 
Equations  (22),  hence  we  can  calculate/,. 

Limiting  Value  for  the  Exterior  Pressure  on  the  Inner  Cyl- 
inder, System  at  Rest. 

It  has  been  stated  that  R^,  given  by  Equations  (22)  represents 
the  maximum  stress  to  which  the  gun  can  be  subjected  in 
action,  the  smaller  of  the  two  values  of  P^  being  used.  It  is 
necessary  now  to  determine  what  value  can  be  allowed  for 
the  exterior  pressure  upon  the  inner  cylinder  at  rest,  so  that 
the  interior  surface  of  the  latter  will  not  be  compressed  by  it 
beyond  its  elastic  hmit.  To  do  this  we  must  find  the  value 
of  Ri   for  the  state  of  rest. 

The  value  of  R/  for  this  state  is  as  has  been  shown 

R/  =R.  +  Pi 

Assuming  Equation  (18)  and  making  P  —  o^  since  the 
interior  pressure  at  rest  is  zero,  we  have 

~2  R""  P' 

A  — 


{R^  —  P')E 


which  shows  since  it  is  negative,  that  there  is  tangential  com- 
pression, and  as  this  is  generally  greater  than  the  radial  com- 
pression. Equation  (18)  only  is  used. 

This  compression  must  not  exceed  that  at  the  elastic  hmit 


40  XIX. — GUN   CONSTRUCTION. 


which  is 

P 

E 
hence  we  have 

for  the  limiting  value  of  the  compression  at  the  interior  of  the 
inner  cylinder.  Changing  the  letters  to  correspond  to  the 
case  of  the  tube  under  discussion ;    that  is,  making 

F'  =  P/ 

R'  ^  R, 

R  ^  R, 

E  ^E, 

P       =   Po 

and  omitting  the  negative  sign,  as  that  simply  indicates  com- 
pression, we  write 

2  R,'  r/  p. 


or 

but 
hence 


(y?.'  -  K)  E^      E, 


^,  ^  (i?,'  -  F?^  p. 


2/C 
^  =  ^.  +  A 


/>/=/».  +  /.  ^  ^^-'^"5^°  (25) 

and  this  value  of  P^  must  not  be  exceeded. 

This  equation  gives  the  value  of  /*/  r=  P^  -("  A  i^^  known 
terms. 

But  we  have  the  value  of /i  from  Equation  (24)  by  substi- 
tuting for /„  its  value  —  P^.  Hence,  substituting  the  value 
of /i  from  Equation  (24)  in  (25),  we  obtain  a  new  value  for 
P^  which  will  cause  the  interior  of  the  inner  cylinder  to  be 
compressed  to  its  elastic  limit  at  rest.     The  value  thus  ob- 


XIX. — aUN   CONStRUCTlOl^.  41 

tained  for  P^  must  be  substituted  in  that  one  of  Equations 
(22)  which  gives  the  least  value  for  P^.  The  new  value  thus 
obtained  for  P^  will  be  such  that  the  inner  cylinder  will  not 
be  strained  beyond  its  elastic  Hmit  either  in  action  or  at  rest, 
and  it  represents  the  greatest  value  of  the  stress  to  which  the 
gun  can  be  subjected  without  exceeding  the  elastic  limit  of 
the  metal  composing  it. 

THE  SHRINKAGE. 

In  Fig.  12,  let  OA  represent  the  interior,  and  OB  the  ex- 
terior radius  of  the  inner  cylinder,  and  OC  and  OD  the  inte- 
rior and  exterior  radii  of  the  outer  cylinder,  before  they  are 
assembled  to  form  the  gun.  Then  the  length  CJS=  OB —  OC 
is  the  shrinkage.  As  diameters  are  usually  employed  instead 
of  radii  in  tables  of  shrinkages,  a  more  usual  expression  for 
the  shrinkage  is 

2  C^  =  2  {OB  —  OC) 

or,  in  other  words,  the  shrinkage  is  the  difference  of  diameters 
of  the  enveloping  and  enveloped  cylinders.  This  is  called 
the  absolute  or  actual  shrinkage.  The  relative  shrinkage  is 
the  shrinkage  per  unit  of  diameter,  or  per  unit  of  radius,  and 
is  expressed  by  dividing  the  absolute  shrinkage  by  the  interior 
diameter  of  the  outer  or  enveloping  cyUnder.  Thus  the  rela- 
tive shrinkage  in  this  case  is 

2CB  ^'^(OB—  OC)      CB 
^0C~         2  0C         ~  OC 

To  determine  the  shrinkage  for  the  case  under  discussion.  In 
Fig.  12,  let  OA,  OB,  OC  and  OD  represent  the  same  quan- 
tities as  above. 

Now,  when  the  outer  cylinder  is  heated  and  expanded  till 
its  interior  radius  OC  is  slightly  greater  than  the  exterior  ra- 
dius OB  of  the  inner  cylinder,  and  the  exterior  cylinder  while 
hot  is  placed  on  the  interior  cylinder,  so  as  to  envelop  it,  and 


4^  XIX. — GUN    CONSTRUCTlOM. 

is  then  cooled  in  this  position,  it  is  evident  that  the  outer  cyl- 
inder will  compress  the  exterior  of  the  inner  one,  and  that 
their  surface  of  contact  will  assume  some  such  position  as 
K  E  E''y  the  outer  radius  O  B  oi  the  tube  being  compressed 
to  O  E^  and  the  inner  radius  O  C  oi  the  outer  cylinder  being 
extended  to  O  E,  Hence  the  radius  O  B  has  been  compressed 
by  the  amount 

OB  —  OE  z=  BE 

and  the  radius  OC  has  been  extended  by 

OE—  0C=^  CE  ' 

and  the  sum  of  these  two  is  equal  to  the  original  shrinkage, 

BC,  or 

BE  -^  CE^  BC, 

Hence,  if  we  can  find  the  values  of  the  two  quantities  BE 
and  CE^  we  will  have  that  of  the  shrinkage. 

Now  when  the  two  cylinders  are  assembled,  and  the  system 
is  at  rest,  we  have  found  that  the  pressure  P^  acts  at  the  con- 
tact surface  of  the  cylinders.  That  is,  the  exterior  cylinder  is 
acted  upon  by  a  force  represented  by  P^,  and  this  force  pro- 
duces an  extension  per  unit  of  radius  of 

CE 

OC 

CE  being  unknown.     But  Equation  (18)  gives  the  value  of 

this  extension  in  terms  of  the  radii,  pressures  and  modulus  of 

the  cylinder.     Remembering  that 

P'  =  P^  —  o 
P  =P,' 
R'  =  R, 
R  =  R, 
E  =E, 
we  write 

CE  _  (4  ^^  +  2  R,')  P! 

OC  ~  3  {Rl  ~  R^')E, 

This  gives  CE, 


XIX. GUN   CONSTRUCTION.  43 

To  find  BEy  or  the  compression  of  the  exterior  of  the  tube. 
The  pressure  acting  is  P/,  as  before,  the  interior  pressure 
being  zero.  This  change  being  at  the  exterior  of  the  cyHnder, 
we  use  Equation  (23),  making  the  following  changes, 

P   =  o 

P'  =  P^ 


Hence  we  have 

E  =E, 

oc  ~  ■^  - 

(4  iP„  +  2  J?,')  P! 
-        3  {R;-  -  Rl)  E, 

Strictly  speaking,  the  true  value  is  -—-  for  the  change  per 

unit  of  radius,  but  the  difference  between  OB  and  OC  '\s  so 
small  in  practice  that  either  may  be  used  without  appreciable 
error. 

Now  it  will  be  observed  that  the  value  of  -^  =  A  just  ob- 

tained,  is  negative,  indicating  compression,  and  this  is  evi- 
dently correct. 

But  the  shrinkage  sought  is  the  sum  of  two  positive  quan- 
tities 

BE  4-  CE        CB 
'OC        ~  ~0C 
In  order  to  avoid  the  negative  sign,  and  obtain  the  quantity 

BE 

j^  under  a  positive  form,  we  suppose  that  the  exterior  cyl- 

inder  is  removed  from  the  interior  cylinder.  In  this  case  it 
is  evident  that  the  exterior  surface  of  the  inner  cylinder  will 
expand  and  regain  its  original  diameter,  and  that  this  expan- 
sion is  exactly  the  same  in  amount  as  the  compression  BE, 
which  was  produced  by  shrinking  on  the  outer  cylinder. 
This  is  equivalent  to  supposing  the  pressure  P^'  neutralized 


44  XIX. — GUN    CONSTRUCTION-. 


by  an  equal  and  opposite  pressure ;  that  is,  in  the  value  of 

BE 

--T.  we  make 

P.'  =  -  A' 
and  that  value  becomes  accordingly — 

BE  _  (4  R^  +  2  R^)  F,' 

a  positive  quantity.  Now  denoting  by  op  the  shrinkage  of 
the  two  cylinders,  we  have 

CE-\.BE      (4^/  +  2i?.^)P/      (4.R:-^<2R,^)P' 
^  OC       ~    ^  (R^'  —  R:')  E,~^S  (R,'  —  R^')  E^  ^  ^ 

In  using  this  equation  it  must  be  remembered  that  cp  is  the 
relative  shrinkage,  or  the  shrinkage  per  unit  of  diameter.  To 
obtain  the  absolute  shrinkage,  the  relative  shrinkage  must  be 
multiplied  by  the  diameter.  That  is,  if  Z>  represent  the  diam- 
eter and  (p  the  relative  shrinkage  (both  in  inches),  and  *S  the 
absolute  shrinkage,  then, 

S  ^  (j)X  z> 

and  the  exterior  diameter  of  the  cylinder  must  be  made 
E>'  =  D-{-  S 
Referring  to  figure  12, 

2  OC^  jD 
2CR=S=q)XZ> 
2  0B=  D' 

GENERAL    REMARKS. 

It  can  be  shown  theoretically  that  the  maximum  resistance 
is  obtained  from  a  gun  cylinder  when  the  radii  of  the  differ- 
ent cylinders  composing  it,  vary  from  the  interior  in  geomet- 
rical progression. 


XIX. — GUN   CONSTRUCTION. 


45 


This,  however,  is  never  adopted  in  practice  for  various 
reasons,  one  of  the  principal  being  the  objection  to  very  thick 
cylinders  on  account  of  their  being  more  difficult  to  forge, 
less  uniform  in  quality,  and  more  liable  to  imperfections  in 
the  metal. 

It  can  also  be  shown  that  no  great  advantage  is  gained  as 
regards  tangential  strength,  by  increasing  the  thickness  of  the 
walls  of  the  gun  over  the  powder  chamber  much  beyond  one 
caliber.  These  considerations  combined  with  the  capacity  of 
the  forging  plant  where  hoops,  tubes  and  jackets  are  made, 
will  serve  to  fix  the  limits  of  thickness  of  the  different  cylin- 
ders composing  the  gun.  Examples  are  given  here  of  three 
modern  guns : 


Gun. 

Diam.  of 
powder 
chamber. 

Thick- 
ness of 
tube. 

Thick- 
ness of 
jacket. 

Thick- 
ness of 
-Whoops. 

Thick- 
ness of 
£  hoops. 

Total 
thickness 
of  wall. 

Total 

thickness 

of  wall. 

Inches. 

Inches. 

Inches. 

Inches. 

Inches. 

Inches. 

Calibers. 

8-in. 

9.50 

2.75 

4.25 

3.30 

10.30 

1.0842 

10-in. 

11.80 

3.20 

4.90 

2.525 

3.10 

13.725 

1.1631 

12-in. 

14.20 

3.90 

5.80 

2.90 

3.425 

16.025 

1.1285 

The  caliber  being  the  diameter  of  the  powder  chamber, 
the  above  table  shows  that  the  thickness  of  wall  only  sHghtly 
exceeds  one  calibre. 

Having  determined  from  the  above  considerations  the 
radii  of  the  different  cylinders  composing  the  gun,  the  values 
of  the  pressures  which  the  gun  will  support  in  action  may 
be  calculated  from  Equations  (22),  B  and  p  being  known 
from  tests  of  the  metal  in  a  testing  machine. 

Having  obtained  the  values  of  /{  and  F^  from  Equations 
(22),  the  system  must  be  considered  at  rest,  and  the  values 
of  the  pressure  P/  deduced  which  will  be  safe  for  that  state 
of  the  system.     This  is  given  by  Equation  (25). 

Then  this  value  of  P^'  must  be  used  to  deduce  a  new 


46  XIX. — GUN    CONSTRUCTION. 


value  of  Z*! ,  and  this  value  of  P^  must  be  substituted  in  that 
one  of  Equations  (22)  which  gave  the  lower  value  for  P^ . 
The  new  value  of  P^  thus  deduced  will  represent  the  maxi- 
mum pressure  to  which  the  gun  can  be  safely  subjected. 

We  can  now  calculate  the  shrinkage  from  Equation  (26), 
using  the  value  of  P/  already  found. 

The  same  method  can  be  extended  to  guns  composed  of 
any  number  of  cylinders,  but  the  subject  becomes  more 
complex  as  the  number  of  cyhnders  increases. 

After  calculating  the  shrinkages,  the  same  fundamental 
formulas  may  be  used  to  calculate  the  compressions  of  the 
bore  produced  by  the  assembhng  of  the  cylinders.  The 
results  of  these  calculations  are  then  compared  with  actual 
measurements  of  the  bore  made  during  the  assembling  of  the 
gun,  and  the  agreement  is  in  every  case  found  to  be 
remarkably  close,  and  furnishes  a  proof  of  the  correctness 
of  the  theory. 


Thickness  of  Gun  at  Different  Points. 

The  thickness  of  the  gun  at  the  reinforce  is  determined  by 
the  considerations  already  given,  and  as  stated,  rarely 
exceeds  one  and  a  half  calibres.  To  determine  its  thickness 
at  various  points  along  the  chase,  it  is  necessary  to  have  the 
'*  pressure  curve  "  of  the  powder  at  different  points  along  the 
bore.  Formulas  have  been  deduced  for  this  curve  by  various 
authors,  but  it  is  not  deemed  necessary  to  give  them  here. 
The  results  obtained  from  them  do  not  agree,  and  recent 
experiments  on  a  small  gun  show  that  Noble  &  Abel's  formula, 
Chapter  IX,  agrees  very  well  with  the  results  of  experiment. 
Using  this  formula,  the  pressure  curve  can  be  obtained. 

The  elastic  resistance  of  the  gun,  or  the  values  of  P^  for 
different  sections  of  the  gun,  are  calculated  as  explamed,  and 
plotted,  and  the  curve  of  powder  pressure  for  the  same  gun 


XIX.— GUN   CONSTRUCTION.  47 

is  also  plotted  to  the  same  scale.     The  curve  of  resistance 
should  always  He  above  the  curve  of  pressures. 

Length  of  Gun. 

This  may  be  determined  for  a  given  initial  velocity  and 
given  conditions  of  loading,  charge  of  powder,  etc.,  by 
Sarrau's  formulas  for  velocity,  but  as  a  practical  rule,  it  may 
be  stated  that  at  present  the  total  length  of  modern  high 
power  guns  varies  between  35  and  45  calibres,  and  that  the 
tendency  is  toward  the  higher  limit. 


XX. — EXTERIOR     BALLISTICS. 


CHAPTER   XX. 

EXTERIOR  BALLISTICS. 

This  treats  of  the  motion  of  the  projectile  after  it  has 
left  the  gun. 
Definitions. 

The  sights  are  two  projections  on  the  upper  surface  of 
the  piece,  the  distance  between  which  parallel  to  the  axis, 
is  called  the  sight  radius^  or  sometimes  the  radius  of  the 
gun. 

Each  sight  contains  a  definite  point  called  the  sight  point. 
That  for  the  front  sight,  which  is  fixed,  is  generally  deter- 
mined by  the  intersection,  at  an  acute  angle,  of  the  faces 
of  a  wedge  or  by  the  intersection  of  cross  wires  as  in  sur- 
veying instruments.  That  for  the  rear  sight  consists  of  a 
notch  in  a  bar,  or  a  pin  hole. 

The  rear  sight  point  is  movable  so  as  to  vary  its  distance 
from  the  axis. 

The  difference  of  the  distances  of  the  sight  points  from 
the  axis  of  the  bore,  divided  by  the  radius  of  the  gun,  meas- 
ures the   tangent  of  the  angle  of  elevation^  or  of  <f,  figure   I. 

The  line  of  sight  is  a  straight  line  passing  through  the  two 
sight  points.  In  the  act  of  aiming  it  also  pierces  the  target. 
In  this  case,  therefore,  the  angle  of  elevation  is  the  angle 
included  between  the  line  of  sight  and  the  axis  of  the  bore. 

The  line  of  departure  is  the  line  in  which  the  projectile  is 
moving  when  it  leaves  the  gun.  It  is  therefore  the  tangent 
to  the  trajectory  at  the  muzzle.  Owing  to  the  incipient 
recoil,  due  to  the  conservatism  of  the  system  (Chapters  VII, 


XX. — EXTERIOR    BALLISTICS. 


XXI),  and  to  necessary  looseness  of  the  joints  between  the 
trunnions  and  the  carriage,  and  between  the  carriage  and  the 
wheels,  the  piece  tends  to  revolve  slightly  about  some  point 
in  rear,  so  that  the  projectile  does  not  always  leave  the  piece 
in  the  original  direction  of  the  axis.  The  angle  included 
between  the  axis  and  the  line  of  departure  is  called  the  angle 
oi  ju7np,j\  figure  1.  If  to  attain  a  given  target  the  jump, 
which  is  almost  always  positive,  were  neglected,  we  would 
find  d'>  q  and  the  computed  value  of  e  would  be  too  great, 
so  that  the  target  would  be  overshot. 

The  angle  made  by  the  line  of  departure  with  the  horizon- 
tal plane  is  called  the  angle  of  departure,  d,  figure  1.  It  is 
with  this  angle  that  we  have  principally  to  deal  in  ballistics, 
as  it  is  the  angle  at  which  the  projectile  actually  begins  its 
flight. 

The  angle  of  projection  is  the  angle  included  between  the 
line  of  departure  and  the  line  of  sight ;  it  may  be  thought  of 
as  the  angle  of  elevation  corrected  for  jump. 

The  quadrant  angle  is  the  angle  made  by  the  axis  of  the 
bore  and  the  horizontal.  It  is  measured  by  the  gunner's 
quadrant,  a  form  of  spirit  level,  applied  to  the  face  of  the 
muzzle  or  to  some  cylindrical  surface  of  the  gun.  Owing  to 
the  grooves  in  rifled  guns  this  is  preferably  an  exterior  surface. 
See  q,  figure  1. 

The  quadrant  angle  may  be  measured  either  above  or 
below  the  horizontal  plane.  The  term  depressed  or  plunging 
fire  refers  to  a  negative  quadrant  angle. 

The  angle  of  sight  is  the  angle  included  between  the  line 
of  sight  and  the  horizontal  plane,  or  s^  figure  1.* 

*  This  depends  solely  upon  the  altitude  of  the  target  in  the  astronomi- 
cal sense.  It  is  unfortunate  that  the  term  above  named  should  be  used 
to  designate  this  angle,  as  it  has  nothing  whatever  to  do  with  the  sights. 

It  would  be  more  consistent  if  the  terms  angle  of  sights  and  of  elevation 
were  exchanged.  In  the  P>ench  service  the  angle  of  sight  is  called  the 
angle  of  site. 


XX. —  EXTERIOR  BALLISTICS. 


It  is  seen  from  the  figure  and  by  definition  that 

Of  these  quantities,  s  is  given  by  the  act  of  pointing,  and 
e  must  be  computed  by  the  methods  hereafter  explained. 
The  above  equation  is  principally  useful  for  verifying  the 
elevation  given  by  the  sights  or  for  guns  which  are  not  pro- 
vided with  sights. 

To  determine  the  Jump, 

Place  in  front  of  the  gun  and  at  a  distance  just  beyond 
the  reach  of  the  blast  a  slight  screen.  Mark  upon  the  screen 
the  point  o^  at  which  it  is  pierced  by  the  axis  of  the  bore 
prolonged.  In  breech-loaders  this  may  be  done  by  means 
of  perforated  discs  fitting  the  bore,  and  in  muzzle-loaders 
by  making  ^  =  0  and  laying  off  on  the  screen  the  coordi- 
nates of  the  sight  points  negatively  taken. 

Fire  the  piece  and  determine   V. 

If  then  X  and  y  are  the  horizontal  and  vertical  coordi- 
nates of  the  center  of  the  shot  hole  when  referred  to  ^,  and 
d  the  distance  of  the  screen  from  the  muzzle  we  have 
approximately,  from  figure  2, 


tan  J  — 


._y  -Vab 


d 


^t^  d 

but  ad=  ^     and     t=  ~   neartyj 

hence  tan  /=  |  +  ^^. 

If  the  shot  strikes  below  the  point,  then  y   is  measured 
negatively. 

X 

The  lateral  jump  is  evidently  tan~^  =  —, 

"  Cti 


XX. — EXTERIOR    BALLISTICS. 


A  number  of  such  determinations  should  be  made  since 
the  method  is  obviously  inaccurate. 

A  better  plan  is  to  eliminate  the  effect  of  the  perturba- 
tions near  the  muzzle  by  computing  e  and  determining  by 
experiment  the  value  of  p  for  an  extended  range  of,  say 
600  yards, — then  j  —  p  —  e 

The  jump  is  usually  about  30'  which  value  will  be  taken 
in  problems  in  which  it  is  required  to  be  assumed. 

The  planes  of  sight  and  of  departure  are  vertical  planes 
containing  the  corresponding  lines. 

The  computed  range  is  the  distance  from  the  gun  to  the 
(second)  intersection  of  the  trajectory  by  the  line  of  sight. 
The  term  range  is  also  applied  according  to  circumstances 
to  the  distance  of  the  target  from  the  gun,  and  to  the  hori- 
zontal distance  to  the  point  of  impact — in  case  the  target 
be  missed  and  the  projectile  strikes  some  horizontal  surface 
in  front  or  rear  of  the  target — such  as  water. 

Practically  the  dimensions  of  the  gun  may  be  neglected 
so  that  the  front  sight  point  may  be  considered  in  the  axis 
of  the  bore  and  the  range  to  be  measured  from  either  sight 
indifferently. 

In  the  following  discussions  we  will  also  assume  that  the 
planes  of  sight  and  of  departure  coincide  in  the  vertical 
plane  containing  the  axis  of  the  piece,  which  is  called  the 
plane  of  fire^  and  that  the  projectile  travels  in  the  plane 
of  departure. 

This  is  not  actually  true,  however,  for  the  projectile  tends 
to  move  sideways  out  of  the  plane  of  departure  as  shown  by 
the  horizontal  projection  of  figure  1.  This  motion,  called 
the  drifts  is  due  to  the  combined  effect  of  the  rotation  of  the 
projectile  and  the  resistance  of  the  air ;  combined  with  other 
causes  of  inaccuracy  it  leads  at  the  target  to  lateral  deviation^ 
which  is  meaured  by  the  distance  of  the  point  of  impact  from 
the  plane  of  sight.     See  Chapter  XXX. 


XX. EXTERIOR    BALLISTICS. 


The  deviation  in  ran^e  is  similarly  measured. 

Classification  of  Fire, 

In  this  classification  the  sights  are  disregarded  and  the 
line  of  fire  is  the  straight  line  from  the  muzzle  of  the  piece 
to  the  point  aimed  at.  Similarly  for  general  discussions  the 
quadrant  angle  is  sometimes  called  the  angle  of  fire. 

Figure  3  illustrates  the  classification  with  reference  to 
the  vertical  plane  containing  the  target,  which  represents  a 
certain  face  of  a  work. 

Figure  4  illustrates  the  classification  with  reference  to 
the  horizontal  plane.  The  limit  for  direct  fire  is  imposed 
by  the  principle  of  the  rigidity  of  the  trajectory  to  be  here- 
after explained. 

The  classification  is  also  applied,  as  indicated,  to  the 
angles  of  descent.  This  is  more  accurate  since  it  relates  to 
the  effect  produced  rather  than  to  the  intention  of  produc- 
ing a  given  effect. 


In  figure  1  it  is  assumed  without  sensible  error,  that  the  lines  of 
sight,  departure,  etc.,  intersect  at  the  muzzle,  and  the  drift  is  very  much 
exaggerated. 


XX. — EXTERIOR     BALLISTICS. 


Exterior  ballistics  is  usually  divided  into  tw©  parts.  1st, 
in  vacuo;  2d,  in  the  air. 

I  TRAJECTORY  IN  VACUO. 

Utility. 

The  first  of  these  is  sufficiently  treated  in  the  course  of 
Mechanics.     Its  practical  utility  is  confined  to  two  cases. 

1st.  That  of  projectiles  of  high  sectional  density  moving 
with  comparatively  low  velocity  as  in  mortars,  since  in  such 
cases  the  loss  of  energy  due  to  the  resistance  of  the  air  may 
be  neglected  where  only  approximate  results  are  required. 
Chapter  XVI,  page  1. 

2d.  Cases  involving  the  flight  of  projectiles  in  the  air,  in 
which  some  of  the  data  are  lacking,  or  in  which  the  velocity 
of  the  projectile  in  one  of  its  component  directions  is  so 
low  that  the  consequent  retardation  may  be  neglected. 

»  USEFUL     FORMULAE. 

The  principal  equations  of  this  kind  which  are  used  in 
this  course  may  be  derived  from  equation  (167),  Michie, 
in  which  we  write,  as  is  customary,  y  for  z, 

^  =  Vsme-st;  (1) 


whence 


j=  Vt  sin  d-  ^r^  (2) 


and  by  placing  -^  =0 


(3) 


for  the  time  to  the  vertex  of  the  trajectory. 


XX. — EXTERIOR    BALLISTICS. 


From  the  symmetry  of  the  trajectory  in  vacuo,  T,  the 
whole  time  of  flight  is  equal  to  2/  or 

and 

Eliminating  V  by  substituting  this  value  in  Equation  (2), 

y^q.(T-i)  (6) 

T  s:  T^ 

If  in  this  we  replace  /by  —  we  have  F=  ^—5 —  (7) 

in  which  jj'  now  becomes  F,  the  ordinate  of  the  vertex. 

That  is,  the  height  of  the  vertex  in  feet  is  nearly  four 
times  the  square  of  the  time  of  flight  in  seconds. 

Equations  (6)  and  (7)  are  important,  and  should  be  re- 
membered, as  they  are  frequently  used  in  approximate  solu- 
tions in  the  air. 

If  in  Equation  (169),  Michie,  rewritten  according  to  the 
usual  nomenclature,  or 

y  =  X  tan  0  —  -r--- ^-^  (8) 

in  which  ^is  the  height  through  which  the  projectile  must 
fall  to  acquire  the  velocity  F,  we  make  j  =  6  wq  may 
determine  the  range  X 

2  V  sin  0  cos  (9  _  V  sin  2  d 

X  =: (y) 

g  g 

Therefore  the  range  will  vary  less  from  variations  in  0,  as 
d  approaches  45°. 
Also,  for  the  same  value  of  B,  as  in  S.  B.  mortars, 
X:  X'  -.'.V^:  V'\ 


XX.— EXTERIOR     BALLISTICS. 


But,  considering  the  powder  as  a  reservoir  of  potential 
energy,  frona  the  equation  of  energy  we  have  approximately 

And  assijming  the  weight  of  the  projectile,  JV,  to  be  con- 
stant for  the  same  piece 

w:  w'v.E'.  E'wV^  \  V'^::X:  X\ 

Therefore,  in  a  S.  B.  mortar  the  charges  are  proportional 
to  the  ranges.  This  is  of  importance  in  regulating  charges 
and  works  well  in  practice. 

If  in  equation  (9)  we  substitute  the  value  of  F  in  equa- 
tion (5),  we  find,  if  we  call  g=32  approximately  and  ^=45°, 
X=16  T'  or 

T=  ^  (10) 

which  gives  a  rule  for  timing  mortar  fuzes. 

RESISTANCE  OF  THE  AIR. 

To  give  an  idea  of  the  pressure  exerted  on  projectiles  in 
the  air  and  consequently  of  the  insufficiency  of  the  preced- 
ing formulae  for  practical  use,  except  in  the  cases  cited;  it 
will  suffice  to  say  that  a  velocity  of  the  wind  of  about  100 
miles  an  hour  is  designated  in  the  Ordnance  Manual  as  a 
"hurricane  that  tears  up  trees,  carries  buildings  before 
it,  etc." 

In  projectiles  moving  with  the  high  velocities  now  attained 
the  pressure  is  over  80  times  as  great  as  that  assigned  to 
the  hurricane. 

EXPERIMENTS  TO    DETERMINE  THE  RESISTANCE    OF    THE  AIR. 

Experiments  have  been  constantly  made  since  Robins, 
called  the  "  Father  of  Gunnery,"  began  to  investigate  this 
subject  about  the  middle  of  the  last  century.     But  these 


:XX. EXTERIOR     BALLISTICS. 


gave  untrustworthy  results  owing  to  the  lack  of  suitable 
velocimeters. 

It  is  upon  the  investigations  of  the  Reverend  Francis 
Bashforth,  conducted  under  the  auspices  of  the  British 
Government  from  1865  to  1880,  that  our  knowledge  of  the 
effects  of  this  resistance  is  based. 

RESULTS   OF    EXPERIMENTS. 

Resistance. 

Bashforth's  experiments  demonstrate  that  the  resistance 
varies  with  the  quantities  shown  on  the  following  tabular 
scheme. 

'1.  Area  of  cross-section  or  ^^,  Chap.  XVI. 

2.  Density  of  air. 

3.  k,  Chap.  XVI,|l.  Meridian  section]^  ^^^^^^^» 


Resist- 
ance 

varies 

with     ^      page  2,  viz.:     |jj    Velocity  of  projectile'. 

1.  That  the  resistance  varies  with  the  area  is  recognized  by 
all  experimenters. 

2.  The  effect  of  variations  in  the  density  of  the  air,  whether 
due  to  variations  in  barometric  pressure,  in  temperature  or  in 
humidity,  or  from  the  passage  of  the  projectile  through  strata 
of  varying  density,  is  allowed  for  m  refined  computations  by 
suitable  coefficients.  For  this  treatise  the  effects  of  such 
variations  are  neglected. 

3.  Variations  in  k  due  to  slight  variations  in  the  meridian 
section  are  also  neglected,  although  they  may  be  similarly 
corrected,  see  b  below. 

1.  As  to  the  Meridiafi  Section^  viz,  : 
(a)  Form  of  Head. — Bashforth  in  his  experiments  used 
projectiles  of  the  same  calibre  and  weight,  and  having  heads 
of  five  different  shapes.  These  were,  1st,  hemispherical; 
2d,  hemispheroidal,  with  axes  in  the  ratio  of  1  to  2; 
3d,  ogival,  radius  of  head  1  diameter;  4th,  ogival,  radius  of 
bead  2  diameters;  5th,  fiat. 


10  XX. — EXTERIOR   BALLISTICS. 

The  resistance  was  greatest  on  the  flat-headed  projectile, 
and  least  on  the  hemispheroidal  and  ogival  of  two  diameters. 
Rashforth  concludes  that  the  resistance  offered  by  the  air  to 
the  motion  of  elongated  projectiles  is  but  little  affected  by 
the  more  or  less  pointed  apex,  but  depends  chiefly  upon 
the  form  of  the  head,  near  its  junction  with  the  cylindrical 
body  of  the  shot.  At  this  point  the  forms  of  the  hemisphe- 
roidal head,  and  of  the  ogival  head  of  two  diameters  radius, 
are  about  the  same,  and  their  resistances  are  nearly  equal. 

(/^)  Form  of  Body. —  Recent  experiments  by  Krupp  have 
shown  that  the  resistance  varies  also  with  the  shapes  of  the 
sides  and  rear  of  the  projectile,  and  with  the  character  of  its 
surface. 


2.  Retardation  and  Velocity, 

Rashforth's  method  was  one  of  interpolation  founded  on 
the  use  of  velocimeters  of  Class  II,  by  which  he  determined 
by  means  of  finite  differences  the  retardation  of  the  pro- 
jectile at  certain  points  of  its  trajectory  at  which  the  velocity 
was  known. 

Everything  else  being  constant,  the  relation  between  the 
retardation  and  the  velocity  was  known  for  each  of  the  veloc- 
ities observed  at  any  one  fire.  And  by  varying  these  veloc- 
ities as  by  varying  the  initial  velocity  or  the  distance  of  the 
gun  from  the  targets,  an  indefinite  number  of  velocities  could 
be  observed  and  their  corresponding  retardations  computed. 

Finally,  the  law  connecting  the  velocity  and  the  retardation 
could  be  deduced  by  analysis,  or  expressed  by  plotting  a 
curve  of  which  the  retardation  and  velocities  are  the  coordi- 
nate axes. 

For  the  same  velocity  the  retardation  was  found  to  vary 
with  (')  the  sectional  density  of  the  projectile,  its  f )  meridian 
section  and  (')  surface,  and  with  the  (*)  density  of  the  air  as 


XX. —  EXTERIOR    BALLISTICS.  11 

affected  by  its  temperature,  barometric  pressure  and  its 
humidity. 

Accordingly,  such  a  law  must  for  convenience  be  reduced 
to  standard  conditions,  that  is,  when  (i)  W  (in  pounds)  =  d^ 
(in  inches),  i.  e.,  when  we  have  the  unit  projectile^  and  when 
the  (2)  proportions  and  (3)  surface  of  the  projectile  are  well 
defined,  and  the  (^)  density  of  the  air  is  at  a  known  standard. 

Variations  in  these  four  conditions  are  subsequently 
allowed  for  by  suitable  empirical  coefficients  of  which  we 
shall  deal  with  only  that  relating  to  the  sectional  density. 

It  may  be  stated  however  that  Bashforth  used  a  M.  L.  R. 
gun  firing  studded  projectiles^  the  points  having  a  radius  of 
IJ  calibres.  The  more  recent  B.  L.  projectiles,  having 
sharper  points  and  smoother  surfaces,  reduce  the  retardation 
by  5  or  .10  per  cent.     See  page  10. 

bashforth's  method. 

,  He  placed  10  targets  at  a  constant  interval  of  150  feet=/. 
This  gave  such  a  number  of  observations  at  each  fire  that 
they  served  to  correct  each  other  by  the  principle  of  con- 
tinuity, so  that  the  final  order  of  differences  would  be  either 
0,  or  would  change  very  slowly.  Examples  of  this  are  seen 
in  the  methods  used  in  correcting  tables  of  squares,  cubes 
and  of  logarithms. 

For  this  purpose  the  advantages  of  instruments  of  Class 
II.  over  those  of  Class  I.  are  obvious.  Such  instruments 
ordinarily  give  only  the  velocity  at  some  point  between  each 
pair  of  targets.  But  Bashforth  sought  the  velocity  at  the 
target  itself  as  follows  : 

Calling  (7;,,)  the  velocity  at  the  target  which  is  at  a  distance 
X  from  the  gun 


12  XX. — EXTERIOR    BALLISTICS. 

In  measuring  velocity  it  is  customary  to  express  j  as  a 
function  of  t,  in  which  t  (one  second)  is  the  constant. 
But  when,  as  in  these  experiments,  /  is  constant,  it  is 
advisable  to  express  the  velocity  by  varying  the  value  of/. 
Consequently,  calling  r^  the  retardation  at  the  distance  x 
and  observing  that,  since  this  is  a  negative  acceleration,  we 
may  neglect  the  minus  sign  resulting  from  differentiation, 
we  have  "^ 


~di~~dF 


^{ij=i^^^  (12) 


The  object  of  presenting  the  retardation  in  this  form  was 
to  make  it  an  explicit  function  of  the  cube  of  the  velocity 
since  Bashforth  had  reason  to  believe  that  the  retardation 
followed  what  is  known  as  the  cubic  law.^ 

In  order  to  apply  equations  (U)  and  (12)  practically,  it 
is  necessary  to  find  by  experiment  such  finite  values  for  dt 
and  d'^t  that,  when  substituted  in  the  preceding  equations 
they  will  give  proper  values  for  v^  and  r,.  Or,  calling  these 
finite  values  A/,  ^nd  AV, 

^^=^  (11') 

'■.=  ~/r^l  (13') 


*  The  simplicity  of  such  a  law  has  always  proved  attractive  to  in- 
vestigators of  thir,  subject.  Sir  Isaac  Newton  took  it  to  vary  with  the 
square  of  the  velocity,  and  others  with  varying  powers  of  the  velocity 
corresponding  to  certain  limiting  velocities. 

Newton's  law  has  recently  been  proved  nearly  true  for  the  high  veloci- 
ties and  smooth  pointed  projectiles  now  employed.  It  will  be  seen  here- 
after how  Bashforth  corrected  the  cubic  law  by  an  empirical  coefficient 
corresponding  to  the  velocity. 


XX. — EXTERIOR     BALLISTICS.  13 


DETERMINATION    OF    VELOCITY    AND    RESISTANCE. 

Referring  to  Bashforth's  experiments,  let  s  denote  the 
distance  from  any  origin  to  the  first  target.  Then  j  +  / 
will  be  the  distance  from  the  same  origin  to  the  second 
target  and  s-\-(n  —  1)  /  the  distance  to  the  «'*  target  at  the 
distance  x,  and  so  on. 

Also,  let  4  denote  the  time  from  any  origin  until  the 
first  target  is  reached.  Then  fs+(n-i)i  will  be  the  time  from 
the  same  origin  until  the  n^'^  target  is  reached  and  so  on. 

Now,  let  ^1,  4>  4>  etc.,  denote  the  1st,  2d,  3d  orders  of 
difference  and  d\  d'\  d"\  the  successive  terms  in  these 
orders  of  difference  so  that  4'"  will  mean  the  third  term 
in  the  second  order  of  difference  and  so  on. 

Then  4+i~4=^/>  which  will  be  the  time  of  passage  of 
the  projectile  between  the  1st  and  2d  targets  and 

4+21       4+1  =  ^1     y 

and  d-l*—d^=d^  and  so  on. 

We  may  therefore  form  the  following  table  which  may 
be  filled  up  from  experiment  as  shown  below  numerically, 
and  graphically  by  the  diagram,  figure  5. 

The  dotted  lines  in  the  diagram  serve  to  indicate  the 
successive  orders  of  difference  after  the  manner  of  the 
brackets  in  the  table. 

TABLE. 

No.  of        -p..  .  Time  of        Orders  of  difference. 

target.         distance.      ^^^^^^^      ^^  ^^  d^     .     ,     ,     d^n-i) 


1. 

s 

^8 

2. 

s  +  l 

4-fi 

3. 

j  +  2/ 

4+21 

4. 

5  +  3/ 

4+31 

5. 

j  +  4/ 

4+41 

[  dJ'  etc. 


\d. 


14  :XX. — EXTERIOR     BALLISTICS. 


NUMERICAL     EXAMPLE. 

times. 

^1 

^. 

^8 

1. 

S 

3.0526 

.1090 

2. 

j+150 

3.1616 

.1114 

.0024 

0 

3. 

J +  300 

3.2730 

.1138 

.0024 

1 

4. 

J +  450 

3.3868 

.1163 

.0025 

0 

6. 

^  +  600 

3.5031 

.1188 

.0025 

6.  .y  +  750      3.6219 

From  the  algebra  we  have 

^.+.=4+H'  +  «  ^^/  +  «^"~;y3~^^4'  +  etc. 

Arranging  the  terms  of  the  second  member  with  refer- 
ence to  n  which  is  arbitrary,  we  have 

4+ni=4  +  «  W-i  4'  +  J  4'-etc.) 

+  ^(4'-4'  +  etc.)  (13) 

Now  /g^nb  being  a  function  of  the  space  (s  +  nl)^  may  be 
developed  by  Taylor's  formula.     Hence  we  have 

/s+ni=/(^  +  «/)  =^«+  ^«^+  -^T2-  +  ^'"- 
or  since,  ds=lf 


2 


Equating  the  coefficients  of  the  first  power  of  n  in  the 
second  members  of  the  two  identical  equations  (13)  and 
(14),  we  have 

<^/s=<^i'-J4'+^^3'~etc.=A4  (15) 


:XX. — EXTERIOR     BALLISTICS.  15 

which  is  the  finite  value  of  dt^  for  the  constant  increment 
of  5. 

In  other  words,  and  as  shown  by  figure  5,  if  Bashforth 
had  taken  d-l  to  be  the  increment  of  time  at  the  first  tar- 
get corresponding  to  ds^  the  velocity  computed  would  have 
been  the  mean  velocity  between  the  1st  and  2d  targets  and 
would  have  been  too  small.  Consequently  this  increment 
is  diminished  by  \  d^ .  This  makes  the  velocity  too  great, 
so  that  \  d^  is  added,  the  approximation  increasing  with. 
the  number  of  targets  employed;  since,  under  the  same 
circumstances,  the  greater  the  number  of  observations,  the 
more  truly  can  the  law  be  determined;  or,  mathematically 
speaking,  the  greater  will  be  the  ±  correction  applied  to 
d^  since  the  greater  will  be  the  number  of  orders  of 
difference. 

Therefore,  for  the  target  at  the  distance  s  or  the  first 
target, 

_  2__  150 ""^^ 

Similarly  for  the  «'*  target  at  the  distance  x  =  s-\- (n — 1)/ 

150 /  ..„ 

""-  -  d^  -  i  4°  +  ^4"  -  etc.-  df,  ^  (_,,,  ^^^^ 

The  number  of  the  targets  at  which  velocities  could  be 
obtained  is  determined  by  the  number  of  targets  employed 
and  by  the  number  of  orders  of  difference  which  the  law  of 
retardation  permits.  If  n'  be  this  number,  then  velocities 
may  be  determined  at  (n  — ;/)  points. 

Similarly,  we  have  the  coefficients  of  the  second  power 

d%  =  d/—dj  +  etc.  =  A  V„  (18) 

and  for  the  «**  target 


rx  = 


-^  AV,  =  p^.(  d^^d,^  +  etc.  )        (19) 


16  .XX. — EXTERIOR     BALLISTICS. 


Example. 

The  velocity  at  the  4th  target  in  the  preceding  table  is 
1304:  and  the  retardation  246.5.* 

RESULTS    OF    THE    EXPERIMENTS. 

If  the  cubic  law  had  held  true  for  all  velocities,  the  co- 
efficient k  in  Equation  (1),  Chapter  XVI,  could  have  been 
replaced  by  some  explicit  function  of  i^. 

But  while  this  was  found  to  be  nearly  true  for  velocities 
between  1100  and  ]350  feet,  it  failed  for  velocities  above 
and  below  these  limits,  as  Bashforth  found  by  increasing 
his  velocities  progressively  from  100  to  2900  feet. 

He  accordingly  introduced  an  empirical  constant  k*  by 
which  to  correct  the  departure  from  the  cubic  law  so  that 

r  —  —  /&'  7/ 

W         ' 

and  as  k'  is  a  very  small  quantity,  he  replaced  it  by 

/ir=  (1000)3  >^', 
so  that 

Table  I  gives  the  value  of  K  for  the  velocities  named 
therein  and  figure  6  is  plotted   from  the   indications   of 
Table  I. 
Example. 

A  12.5  inch  shell  weighing  802.25  lbs.  has  a  velocity  of 
1400.  The  total  air  pressure  is  1394  lbs.  and  the  retardation 
is  55.96  at  the  instant  that  the  velocity  is  1400. 

Figure  7  gives  the  pressure  on  what  is  called  a  circular 
inch  (that  is  a  circle  of  which  ^=1  inch)  on  spherical  pro- 
jectiles, curve  A;  on  studded  oblong  projectiles  of  which 

*Throughout  this  chapter  velocities  will  be  expressed  numerically,  as 
the  unit  of  velocity,  or  foot-second,  may  be  understood. 


XX. — EXTERIOR    BALLISTICS.  17 

the  radius  of  curvature  of  the  head  is  |  d^  curve  B ;  and 
on  modern  smooth  b.  1.  projectiles  in  which  the  radius  =  2  d, 
curve  C,  derived  from  recent  experiments  by  Krupp. 

In  curve  B  two  remarkable  inflections  are  observed.  One 
at  about  1090,  the  velocity  of  sound,  and  the  other  at  about 
2413,  that  of  air  rushing  into  a  vacuum. 

The  first  velocity  marks  the  passage  of  the  projectile  into 
a  medium  undisturbed  by  the  explosion  of  the  gun  or  by  its 
own  passage.  The  second  denotes  the  formation  of  a 
vacuum  in  rear  of  the  projectile  which  increases  the  pressure 
to  ajDout  double  that  of  the  barometric  pressure  of  the 
atmosphere. 

In  firing  at  troops,  particularly  in  sieges,  it  is  important 
to  have  the  terminal  velocity  exceed  that  of  sound,  so  that 
the  projectile  may  precede  the  warning  sound  made  by  its 
passage  through  the  air. 

The  irregularity  of  curves  B  and  C  shows  the  impossibility 
of  expressing  by  any  simple  law  the  relation  between 
velocity  and  pressure. 

i 
Final  Velocity. 

Figure  7  enables  us  to  appioximate  closely  to  the  final 
velocity  of  the  projectile. 

This  term,  which  must  be  carefully  distinguished  from 
the  ter7ninal  velocity  (Chap.  I),  is  that  velocity  which  the 
projectile  has  acquired  in  falling  when  the  resistance  of  the 
air  becomes  equal  to  the  accelerating  force  of  gravity.  This 
velocity  is  necessarily  uniform  and  a  maximum. 

For  example,  a  64  lb.  projectile,  6.3  inch  in  diameter,  has 
a  weight  per  circular  inch  of  1.613  lbs.  If  it  belongs  to  the 
class  of  projectiles  used  by  Bashforth,  an  equal  and  contrary 
air  pressure  will  result  when  a  velocity  of  nearly  900  f.  s. 
has  been  acquired.  But  for  more  modern  projectiles  a 
higher  final  velocity  will  result. 


18  XX. — EXTERIOR    BALLISTICS. 

This  velocity  which  formerly  had  only  a  theoretical  signifi- 
cance, is  becoming  important  in  consequence  of  the  great 
heights  and  high  angles  of  fire  now  used  in  mortar  firing. 

The  S.  C.  Mortar  has  thrown  its  shell  over  3  miles  into 
the  air  with  an  angle  of  fall  of  about  75°. 

The  result  can  be  reached  more  exactly  by  a  method  of 
approximation  based  upon  the  fact  that  K  enters  into  equa- 
tion (20)  in  the  first  power  while  v  is  cubed.  Consequently, 
the  first  trial  values  of  K  will  not  greatly  affect  the  result, 
and  we  may  finally  find  a  velocity  and  corresponding  value 
of  K  which  will  satisfy  the  eqi^-^Hon 


TRAJECTORY  IN  AIR. 

GENERAL   SOLUTION. 

Notation. 

Let  O  VR  =  S,  figure  8,  represent  a  trajectory. 

Let   V  be  the  muzzle  velocity  in  the  line  of  departure. 

ds 
Let  v=  —j-he  the  velocity  in  the  direction  of  the  tangent 

at  any  point  of  which  the  coordinates  are  x  and  y. 

Let  u  be  the  horizontal  component  of  the  velocity  v. 

Let  7j\  v'\  u\  2^",  be  the  corresponding  tangential  and 
horizontal  velocities  at  the  beginning  and  end  of  any  arc, 
the  coordinates  of  the  extremities  of  which  are  {x*^  y), 
{x",y"). 

Let  (p  be  the  variable  inclination  to  the  horizontal  of  the 
tangent  to  the  trajectory;  then  u^v  cos  (p. 

Let  6  and  g9,  measured  as  in  the  figure,  be  the  particular 
values  of  q)  for  the  angles  of  departure  and  of  fall. 


XX. EXTERIOR    BALLISTICS.  19 

Let  a  and  /?  be  the  values  of  q}  at  the  beginning  and 
end  of  any  arc  when  the  velocity  is  v'  and  v". 

Then  the  figure  shows  that  6  —  a  —  ^  or  the  angle  in- 
cluded between  the  tangents  is  the  change  in  inclination 
due  to  a  change  in  velocity  from  v*  to  v'\ 

Similarly  A=^— (—<»)  =  ^+co  is  the  total  change  in 
inclination. 

Let  q)  (read  (p  "  dash ")  be  the  inclination  to  the  hori- 
zontal of  any  chord  of  the  trajectory. 

Let  2/=  =  =  u  sec  cp  be  the  component  velocity  of 

cos  (p 

V  in  the  direction  of  the  chord,  and,  as  above,  let  v\    v"  be 

the  component  velocities  in  the  direction  of  the  chord  at 

the  beginning  and  end  of  the  arc  (^',^')j  (^">  ^")- 

Let  /,'  /"  be  the  times  measured  from  any  origin  to  the 

instants  when  the  velocities  are  respectively 

(  z/',  z/"),  P",  v^),  etc. 

Note  that  /">/',  v''<v'. 

Let  t—t"—t'  for  any  arc  and  r=time  to  vertex,  T\-\- 
time  from  the  vertex  to  R^  T^  be  the  whole  time  of  flight,  or 

Similarly, 

Let  Jf',  y,  be  the  computed  coordinates  of  the  vertex 
measured  from  0\  and  X^,  K^,  the  computed  coordinates 
of  the  same  point  measured  from  ^,  so  that  the  computed 
range,  X=0 R=X' -^-X^. 

The  figure  shows  that  the  notation  of  z;',  «',  cp^  changes 
from  the  ascending  to  the  descending  branch  to  z'^,  u^^  cp. 
This  distinction  will  be  observed  throughout  when  the 
branches  are  separately  considered;  but,  when  the  trajec- 
tory is  considered  as  a  whole,  v\  z;",  «&c.,  refer  to  the 
beginning  and  ending  of  any  arc. 


20  XX. — EXTERIOR     BALLISTICS. 

Let  the  ordinate  at  D  represent  the  height  of  a  target  at 
the  distance  OD.  Then  DR  is  the  dangerous  space  for 
that  target.  If  we  aim  at  the  center  of  the  target  this 
evidently  measures  nearly  twice  the  ±  error  permissible 
in  estimating  the  distance,  as  a  measure  preliminary  to 
determining  the  value  of  d  required  to  strike  the  target  at 
some  point  of  its  height.     See  Chap.  I.,  p.  3. 

The  dangerous  space  is  known  herein  as  D.  S, 

Eesolution  of  Motion. 

Let  AIR,  figure  9,  be  some  arc  of  the  trajectory  to 
which  //is  the  tangent  at  /,  p  is  the  radius  of  curvature, 
g  the  acceleration  due  to  gravity,  r  the  retardation  due  to 
the  resistance  of  the  air. 

Then  from  the  figure,  for  the  horizontal  retardation, 

-— -  =  r  cos  (p  (21) 

and,  from  Mechanics,  for  the  normal  component  of  the 
deviating  force  of  gravity  ,^^ 

(32) 


-=gcos  cp 

,        1         dcp    .     dt 

but  -  = -/-  X  -77 

p       ds        dt 

=  — ^  and.  therefore, 
dt.v 

dcp 

(23) 

Dividing  Equation  (23)  by  (21)  member  by  member,  we 
have,  after  transposing, 

dq>=  1^  (24) 


XX. — 'EXTERIOR     BALLISTICS. 


21 


Integrating  between  the  limits  (p=^a  and  ^=/5  and  the 
corresponding  values  of  u^  we  have 


/3  y    nf' 


or 


A  ^g 


du 
rv' 


From  equation  (21)  we  have  by  similar  means, 


du 


r  cos  q) 


or 


du 


cos  q) 


Similarly,  from  the  relations  between  x,y,  t,  and  Uy 


u  dt^=- 


u  du 
r  cos  q) 


or 


u  du 
rcos  (p 

u  du 


or 


r  cos  cp 


u  du 
r  cos  cp 


tan  ^, 


tan  ^. 


(25) 
(25') 

(36) 
(26') 

(27) 

(27') 
(28) 

(28') 


22  XX. — EXTERIOR    BALLISTICS. 

If  these  general  equations  (25-28)  could  be  integrated, 
they  would  give  the  change  in  the  coordinates  of  an  arc  of 
the  trajector}'-  (x^'—x^),  (7"— j^')  corresponding  to  a  change 
of  horizontal  velocity  {u^—u")^  the  time  t  required  to 
make  this  change,  and  the  change  of  inclination  d,  corre- 
sponding to  the  same  change  in  the  velocity. 

But  the  second  members  contain  three  variables,  u,  cp^ 
and  r,  not  connected  by  any  law,  and  hence  the  integration 
is  impossible. 

Bashforth's  experiments,  however,  give  the  law  connect- 
ing u  and  r,  and  in  order  to  avoid  the  difficulty  arising 
from  the  presence  of  the  variable  cp  we  assume  for  it  a 
constant  mean  value  qy.  That  is,  that  on  the  same  princi- 
ple as  that  by  which  we  have  neglected  the  small  vertical 
component  of  the  resistance,  we  now  neglect  the  small 
component  velocity  in  a  direction  at  right  angles  to  the 
chord,  and  suppose  the  length  of  the  arc  to  be  that  of  the 
chord,  although  its  curvature  is  retained. 

COROLLARIES. 

I.  Equation  (23)  may  be  written 
d(p __g cos  (p 
~dt  V      ' 


whence,  by  dividing  member  by  member  by 
cos  ^,  w 
dqp  __g 


dx 

-—=zv  COS  cpf  we  obtain 


sul 
dcp  _W 


Calling  esc-  -^ —   and  substituting  we  have 


dx       'Ze 


(30) 


XX. — EXTERIOR   BALLISTICS.  23 

Equations  (29)  and  (30)  express  the  rate  of  change  of  the 
direction  of  the  tangent  to  the  trajectory,  or  the  rate  at 
which  the  trajectory  is  becoming  curved,  as  a  function  of 
the  range.  Equation  (29)  ilhistrates  the  remarks,  Chap.  I, 
top  page  3,  and  Equation  (30)  explains  the  importance  of 
Chap.  XVI,  p.  1.  These  equations  set  forth  a  most  import- 
ant property  of  the  trajectory  in  air. 

Figure  10,  >vhich  is  carefully  drawn  to  a  scale,  represents 
in  curve  A  the  trajectory  in  vacuo  of  a  projectile  fired  with 
e  =  30°  and  V  =  about  1700  f.  s. 

Curves  B  and  C  represent  the  trajectories  m  air  of  spher- 
ical projectiles  as  follows  : 

B.  15  inch ;  W=  450  lbs.  d  =  14.87  inch.  \V=  1700 

C.  24  pdr.  ;   W  =  26.92  lbs.  d  =  5.9  inch.  5  (9  =  30° 
Since  from  Chap.  XVI,  p.  2,  the  elements  of  a  trajectory 

;When  6  and  V  are  given  depend  on  the  ballistic  coefficient 

■— r,  It  appears  that  the  24  pdr.  projectile  would  describe 

the  trajectory  B  if  its  weight  were  increased  to  70.86  lbs., 
the  calibre  remaining  constant;  or,  by  reducing  the  calibra 
to  3.637  inches,  the  weight  of  the  projectile  remaining  con- 
stant.    The  objections  to  this  are  given  Chap.  XVI,  p.  4. 

II.  If  in  equation  (29)  we  substitute  for  2^  its  value 
\p  g  cos  (pf  we  find 

dg)  1  J  dx 

-~  = or  d  o)  cos  (Z)  =  — 

dx      p  cos  (p  ^         ^       p 

Integrating  this  equation  between  the  limits  -(-  6  and  —  w, 
figure  8,  corresponding  to  O  and  X,  and  assuming  some  mean 
value  of  p  =  p'  by  which  to  measure  the  flatness  of  the  tra- 
jectory, we  have  as  a  measure  of  its  mean  curvature, 

1    _  sin  0  +  sin  6> 

7"  -        X  ^^^^ 


24  XX. — EXTERIOR     BALLISTICS. 

Although  from  equation  (22)  and  from  experience  it  is 
evident  that,  owing  to  the  variable  value  of  g  cos  cp^  with 
the  sight  set  for  a  certain  range  it  is  impossible  to  hit  any 
desired  point  of  a  vertical  circle  described  about  the  gun 
with  the  range  as  a  radius;  yet,  as  shown  by  equation  (31) 
and  figure  11,  if  the  altitude  of  the  target  or  the  angle  of 
sight  s,  be  small,  the  decrease  of  g>'  tends  to  compensate 
for  the  increase  of  6',  so  that  sin  6'  +  sin  w'  may  not  differ 
greatly  from  sin  6  -\-  sin  w  :  OX'  =  OX  cos  s  will  also  be  very 
nearly  equal  to  X,  Under  these  circumstances  the  two  values 
of  p'  will  not  differ  greatly  from  each  other. 

Under  this  assumption  we  may  consider  the  mean  curva- 
ture of  the  trajectory  to  be  constant  or  the  trajectory  to  be 
practically  rigid,  so  that  for  small  altitudes  the  elements  of 
the  trajectory  measured  along  the  chord  may  be  safely 
assumed  to  be  independent  of  the  inclination  of  the  chord 
to  the  horizon. 

Equation  (30)  shows  that  this  assumption  will  increase 
in  truth  when  the  sectional  density  and  the  muzzle  velocity 
increase,  which  is  the  present  tendency.  The  principle 
involved  is  of  especial  importance  in  the  rapid  fire  of 
modern  small  arms  and  field  pieces,  since  it  permits  the  use 
for  inclined  ranges  of  sights  graduated  for  horizontal  ranges, 
when  the   ±  angle  of  sight  is  less  than  about  10°. 

In  such  cases  the  change,  s'  figure  11,  in  the  angle  of 
departure,  may  for  a  first  approximation  be  safely  taken  to 
be  equal  to  s,  and  this  change  is  automatically  made  by  the 
act  of  pointing. 

Actually  however,  when  s  is  positive,  p'  decreases  and 
conversely;  so  that  in  firing  up  hill  the  projectiles  tend  to 
fall  short  and  in  firing  down  hill  they  tend  to  pass  over  the 
object. 


XX. EXTERIOR    BALLISTICS. 


NIVEN'S  METHOD. 

Various  expressions  have  been  deduced  for  the  value  of  0 ; 
that  of  Mr.  W.  D.  Niven,  F.R.S.,  obtained  from  an  expand- 
ing series,  is  one  of  the  most  simple  and,  for  illustration,  a 
particular  value  of  0,  deduced  for  equation  (25),  is  herein 
applied  to  all  cases  indifferendy. 

The  appendix  to  this  chapter  contains  the  means  of  arriv- 
ing at  more  exact  values  of  cp. 

Under  this  hypothesis  we  shall  adopt,  as  a  sufficient  approxi- 
mation for  small  angles  of  8  less  than  about  3°, 

0  =  ^,  (32) 

and  for  larger  angles  the  approximation 

—       tan  a  -\-  tan  6  ^,«„x 

tan  0  = J- -.  *(33) 

From  the  notation  we  have 

u  =  V  cos  0 ;     du  =^  dv  cos  0 ;     v'  =  u'  sec  0,      etc. 
Substituting  these  values  in  equation  (25),    and  replacing 
r  by  its  new  value  -^ -^r[TK()()]  '  ^^  ^^^^ 


S  =  cos  (pg 


*  These  values  of  (p  give  good  practical  results. 


26  XX. — EXTERIOR     BALLISTICS. 

In  this  equation  ^  is  expressed  in  circular  measure,  that  is, 
in  terms  of  the  ratio  tt  =  180°.  To  reduce  it  to  the  corre- 
sponding number  of  degrees,  d,  we  have, 

Ttd 
d:7c::d:180     or     ^  = -^^. 

loO 

Substituting  this  value  of  S  in  the  above  equation,  and 
representing  as  hereafter  the  ballistic  coefficient  ^  by  C,  we 
have,  after  reduction, 


^ ,      cos  0  180^  (1000) 

Ca  = 


7t 


In  this  ^  is  a  function  of  v,  and  therefore  changes  between 
the  limits  of  integration.  Means  have,  however,  been  found 
for  determining  its  mean  value  for  limiting  velocities. 

The  value  so  determined  is  nearly  its  arithmetical  mean. 
Therefore  we  have,  calling  this  mean  value  K\ 

^^^cos0i8^o_oo):  r-s^ 

Similarly,  we  have 

And  representing  by  s  the  length  of  the  chord,  the  co-ordi- 
nates of  the  extremities  of  which  are  {x'  x")     (/  y") 

csj^'  ry}         (36) 


We  have  also 


X 


II 


s  cos  0  andji/  =  y"  — /  =  s  sin  (p 


XX. EXTERIOR     BALLISTICS.  27 


These  equations  are  in  a  form  to  be  integrated,  and  Tables 
II,  III,  IV  have  been  computed  for  a  projectile  in  which 
^  =  1,  as  follows  : 

Assume  any  velocity  v^  sufficiently  low  as  the  origin  of  in- 
tegrals, and  assigning  proper  values  for  K',  integrate  equa- 
tions (34,  35,  36)  between  v^  and  successive  values  of  v'. 
We  thus  obtain  what  are  called  angular  /unctions  dy> ,  time 
functions^  r^> ,  and  space  functions,  (Ti/ ,  which  may  be  ex- 
plained by  reference  to  the  time  functions  in  Table  II. 


Explanation  of  the  Tables. 

Considering  the  acceleration  to  be  positive.  Table  II  may 
be  considered  to  express  by  its  functions  the  several  times 
r,  r',  r",  etc.,  required  to  give  to  a  unit  projectile,  starting  as 
from  rest,  the  several  corresponding  velocities  under  the  ac- 
tion of  a  variable  force  equal  to  the  variable  resistance  of  the 
air. 

Table  III  may  be  similarly  understood  to  express  the  space 
in  feet  <t,  a',  a",  etc.,  over  which  such  a  force  would  have  to 
act  in  order  to  increase  the  velocity  from  some  initial  velocity 
as  0,  to  the  several  corresponding  velocities  given. 

It  is  evident  that  each  function  in  each  table  might  be 
numerically  diminished  by  the  first  function  in  its  own  table 
without  affecting  the  value  of  the  table  or  the  velocities  to 
which  it  applies,  since  it  is  only  the  differences  between  func- 
tions that  are  considered. 

Conversely,  considering  the  acceleration  as  negative,  if  any 
time  function  as  r',  figure  12,  measured  from  any  origin  /^ , 
corresponds  to  a  change  v'  —  v^  in  the  velocity  measured 
from  any  origin  v^ ,  and  r"  similarly  corresponds  to  a  change 
r"  —  v^ ,  then  r"  —  r'  can  correspond  only  to  the  particular 
change  &'  —  v".  So  that  knowing  r"  —  r'  ^=^t,  and  either 
z/  or  v",    we  may  determine  the  other  velocity;    and  con- 


28  XX.' — EXTERIOR     BALLISTICS. 

versely  as  to  /,  r',  or  r",  without  regard  to  whether  the 
difference  is  positive  or  negative. 

Similarly  for  the  angular  functions.  If  any  angular  func- 
tion d',  figure  13,  corresponds  to  a  change  v'  —  v^,  and  d" 
to  a  change  jy"  —  v^ ,  then  6*  —  d"  =  ^  will  correspond  to  a 
change  v'  —  v". 

In  all  cases  we  have  two  pairs  of  unknown  quantities,  of 
which  the  difference  between  one  pair  and  one  of  the  other 
quantities  is  needed  to  determine  the  remaining  quantity. 

These  data  are  given  by  the  conditions  of  the  problem,  or 
are  suppHed  by  certain  assumptions  to  be  hereafter  explained. 

Example  from  Table  II. 

The  change  of  time  (or  time  required)  for  a  change  of 
velocity  of  300  when  the  greater  velocity  is  1400  is  231.9883 
—  230.5314  =  1.4569  sec.  When  the  lesser  velocity  is  1400 
it  is  0.8697. 

If  in  the  first  case  the  time  from  some  given  origin,  say  the 
firing  of  the  piece,  until  the  velocity  was  reduced  to  1400  was, 
say,  2  seconds,  then  the  time  measured  from  the  same  origin 
until  the  velocity  fell  to  1100,  would  be  3.4569  sec,  and  so  on. 

PRACTICAL    FORMULAE. 

For  the  ascending  branch  Equations  (34),  (35),  (36)  may  be 
written.* 

Cd  —  cos  (p{di>  —  6-^") ;  (I) 

a  =  r->  —  T^n  ;  (II) 

Cs  =  a^>  —  <T~v".  (Ill) 

Whence  from  III, 

Cx  =  Cs  cos  0  =  cos  0(cr^/  —  (Tin);  (HI') 

Q/  =  Cs  sin  0  =  sin  0(cr;,/  —  (T^"),  (HI") 

*  Similar  equations  serve  for  the  descending  branch. 


XX. EXTERIOR     BALLISTICS.  S9 


The  Greek  letters  in  the  second  members  of  the  above 
equations  are  the  corresponding  tabular  functions  found 
respectively  in  Tables  IV,  II,  III. 

These  tables  are  arranged  like  logarithmic  tables.  Except 
■where  small  changes  of  the  functions  are  considered,  for  sec- 
tion-room work  the  column  of  differences  need  not  ordinarily 
be  employed,  the  nearest  function  or  velocity  being  taken. 

It  is  evident  that  the  nearer  the  chord  is  to  the  arc,  the  less 
will  be  the  difference  v  —  v,  and  the  more  accurate  will  be 
the  result.  In  practice,  it  is  considered  sufficiently  accurate 
to  divide  the  trajectory  into  two  arcs,  at  the  vertex. 

For  simplicity,  and  by  the  principle  of  the  rigidity  of  the 
trajectory,  unless  otherwise  stated,  the  chord  is  taken  hori- 
zontal. 

It  is  important  to  note  that  although  ranges  are  generally 
given  in  yards,  the  chords  of  trajectories  (Chapter  I)  are  ex- 
pressed in  FEET.  Neglect  of  this  frequently  leads  to  failure  in 
practical  work. 

Example. 

To  illustrate  the  use  of  the  tables  in  calculating  the  elements 
of  a  trajectory,  we  will  take  the  100-ton  Armstrong  gun  and 
consider  figures  8'  and  14. 

Data. 

V=  1833;  d  =  ll°50'=ll°.83i;  PF=2005  lbs.;  ^*=17  in.; 

hence 

C=  0.14414,      log-^  =  T.  15879,       co-log -^  =  10.84121. 

This  quantity  must  always  be  determined  before  any  other 
work  is  attempted. 


*The  d  above  must  be  distinguished  from  the  angle  d  elsewhere 
discussed, 


30  XX. — EXTERIOR     BALLISTICS. 


Elements  required. 

1.  The  remaining  energy  at  any  point  or  :  e, 

2.  Height  of  trajectory  at  any  point  ot y. 

3.  Total  range  or  X. 

4.  Angle  of  fall  at  end  of  range  or  qd. 

5.  The  dangerous  space,  D.  S. ,  for  any  range. 

6.  Time  of  flight  to  any  distance  or  /. 

7.  Tinxe  of  flight  for  the  whole  range  or  T. 

8.  Inclination  of  the  trajectory  at  any  distance  or  <p. 

9.  Having  the  initial  velocity  to  find  the  value  of  B  to  at- 
tain a  desired  range. 

etc.  etc.  etc. 

1st.  To  find  the  remaining  energy,  we  find  the  remaining 
velocity  as  follows  : 

From  figure  8  the  change  of  0  from  the  origin  to  the 
vertex  is  ^  =  «  =  d.  At  this  point  /?  =  0  ;  therefore,  from 
equation  (33), 


-       tan  Of  4-  tan  0      tan  11°  50' 

tan  <2!>  =  —  '  — 


2  2 

=  tan  5°  58'  50"  =  tan  5°  58'. 83. 

As  we  shall  have  to  use  the  logarithmic  functions  of  0,  we 
now  tabulate  them  as  follows  ; 

logs.  co-logs, 

sin  T.  01783  10.98317 

cos  1.99763  10.00237  =  log  sec  0. 

To  find  v'  we  project  V  on  the  horizontal  or  determine 
«'  =  Fcos  B\  thence  v'  =  «'  sec  0,  or  «'  =  1794,  v'  =  1803.9. 


XX. — EXTERIOR    BALLISTICS.  31 

Now  to  find  v''  we  transpose  equation  (I)  to  read 

COS    0 

in  which 

Oj,'   =   0 1803.9  • 

In  Table  IV  we  find 

di803  =  84°.8199 
p.  p.  for  0.9  =  21 


84°.  8220 


Consequently,    all  the  quantities   in  the   second   member 
being  known,  we  may  write 

0  14414 
6-r=  84°.8220  -  ll°.83i      ^--l-**-^* 


log'-i  1.99763 
=  84°.8220  -     1°.7149  =  83°.1071. 

From  Table  IV,  again,  we  have  for  the  velocity  correspond- 
ing to  d  =  83°.1071,  v"  =  1318  for  the  remaining  velocity 
at  the  vertex,  and  hence 


«"  =  1318  cos  0  =  1310.8. 

The  origin  is  now  transferred  to  the  vertex,  and  we  treat 
the  descending  branch  similarly  to  the  ascending  branch. 

The  angle  a  for  this  arc  is  evidently  0,  and  u^  =  u"  just 

found,  but  the  value  of  /?  =  g?  required  to  find  0  is  unknown. 

It  is  therefore  necessary  to  assume  a  value  for  it.     Equation 

(29)  shows  that  it  will  be  greater  than  ^,  and  experience 

4^ 
proves  that  it  is  nearly  —  or  a?  =  15°.  77, 


3S  XX. — EXTERIOR     BALLISTICS. 

If  we  assume  an  incorrect  value,  as  will  generally  be  the 
case,  the  error  is  corrected  by  a  subsequent  operation.  So 
let  us  assume  an  incorrect  value,  or  co=  16°,  as  a  first  ap- 
proximation.    Thence 

tan  16°  oo  n/  K 

tan  (p  =  — - —  =  tan  8    9'.  5 
—  4 

I 
and 

v^  =  1310.8  X  sec  8°  9'.5  =  1324.1  and  (J-  ==  83°.1406. 
Using  equation  (I)  again,  we  have 


*,„  =  sr.im  -  ^-5^-5 16° 

=  83°.1406  -  2°.3298  =  80°.8108; 


and  v^^  =  1061,  u^^  =  1050,  and  v^^ ,  the  velocity  along  the 
tangent,  :=  u„  sec.  w  =  1093.  The  vertical  component  of  v 
will  be  =  «yy  tan  w  =  301. 

The  component  energies  are  generally  useful  for  doing  work 
against  targets  which  are  nearly  vertical,  as  the  walls  of  vessels 
or  forts ;  or  horizontal,  as  the  decks  of  vessels  or  the  roofs  of 
magazines  or  casemates.  We  therefore  find  that  while  the 
projectile  started  with  energy  in  the  direction  of  the  tangent 
or  ^y  =  46,700  foot-tons,  it  now  has  ^e/,,  =  16,604  foot- 
tons  ;  only  about  one  third  as  much  as  when  it  started. 

Its  component  horizontal  and  vertical  energies  are  15,320 
foot-tons  and  1260  foot-tons,  respectively. 

The  steps  of  the  problem  can  be  clearly  followed  in  the  first 
stages  of  Example  I,  which  is  given  in  the  form  used  for 
written  recitation. 


XX. — EXTERIOR     BALLISTICS. 


S3 


la. 


Data:    F=1833;    ^  =  11°  50' ;     W=2005;    ^=17  in. 
Required  U^,^^. 


Statement  of  Steps. 

Terms. 

Quantities. 

Functions. 

Logs. 

I-  C  =  ^=0.14414 

c 

T 

17^ 
2005 

O.14414 

2 . 46090 
3 -30211 

1.15879 

c 

IO.8412I 

-      tan  9 
2.  tan0= 

=  tan  5°  58'. 83 

tan  B 

tan  11°  50' 
2 

9.32122 
.30103 

tan  0 

tan  5°  58'.83 

9.02019 

cos  0 

I 

cos 

sec         " 

9-99763 

cos  0 

10.00237 

sin  0 

I 

sin  0 

cos  6 

sin 

9.01782 

I          ,, 
sin 

10.98317 

3.  u'=  F'cos  0  =  1794 

cos  II    50 

1794 

3-26316 
9.99067 

3-25383 

4.   v'  =  u'  sec  (p  =  1803.9 

sec  0 

v 

1803.9 

10.00237 

3-25620 

^■'-^■-'-"-co%-'^^' 

h' 

5l803.9 

84.8220 

C 

d 

n^83i 

1. 15879 
1.07300 

sec  0 

10.00237 

I3I8 

I. 7146 

0.23416 

83.1074 

34 


XX. EXTERIOR     BALLISTICS. 


Statement  of  Steps. 

Terms. 

Quantities. 

Functions.       Logs. 

6.    u'  =:  «^  =  v"  COS  0 

=  I3IO.8 

COS   0 

1318 
1310.8 

1   3-II992 
9.99763 

3.I1755 

7.tan^='^"/  =  8"9'.5 

tan  /? 

tan  0 
cos  0 
sec  0 
sin  0 
I  ~~ 

tan  16° 

tan  8°  9'. 5 
cos       " 
sec      '* 
sin       '* 
I          ., 
sin 

9-45750 
.30103 

9.15647 

9-99558 

10.00442 

9.15201 

sin  0 

10.84799 

8.  vi  =  u  sec  0  =  1324. 1 

sec  0 

1310.8 
1324-2 

3-11755 
10.00442 

3.12197 

9.   d-    =  (5-   —  CJ  sec  0 

=  1061 

d 
sec  0 

^1324. a 

16" 

I06I 

83.1411 
2.3298 

1. 15879 

I. 20412 

10.00442 

The    determination    of    g   is 
omitted. 

0.36733 

80.8113 

XX. EXTERIOR     BALLISTICS. 


35 


lb. 


Data  as  in  la. 

Required  »  at  1000  yards  =  3000  feet. 


Statement  of  Steps. 

Terms. 

Quantities. 

Functions. 

Logs. 

J.    Determine     whether    to 
use  0  or  0  by   finding 
whether  3000  is  <  or  > 
X'  .: 

cos  0 

I 
C 

X' 

O"i803-9 
15045 

44456.3 
42275.8 

9.99763 

jr'=cos0(a--,-o--„)X^ 
=  15045  ft.  =;=  5015  yds. 

.*.  use  0 

2180.5 

3.33856 

IO.84121 

4.17740 

2.  0--,,  =  (T-,  —  Cx  sec  (p 
v"  =  1697 

sec  0 

3000 

1697 

44456.3 
434-8 

I. 15879 
3.47712 

10.00237 
2.63828 

44021.5 

36 


XX. — EXTERIOR    BALLISTICS. 


Data  as  in  la. 

Required  V  from  data  of  ascending  branch. 


Statement  of  Steps. 

Terms. 

Quantities. 

Functions. 

Logs. 

y:=Y' 

=  sin  0(o--,-o--„)i 

sin  0 

9.01782 

^1576.1  feet. 

^i' 

Cri803.9 

44456.3 

^-." 

cri3i8 

42275-8 
2180.5 

3-33856 

C 

IO.84121 

v 

1576. I 

3-19759 

Similarly  we  may  find  from  the  value  of  0  that 
r,  =  1713  feet. 

The  difference,  1713  -  1576.1  =  136.9  is  evidently  due  to 
the  error  in  our  assumption  of  the  value  of  gj,  and  therefore  in 
our  deduced  value  of  0 ;  the  effect  is  to  increase  the  range  as 
shown  by  figure  14. 

This  leads  to  the  means  of  correcting  od  to  be  explained. 

3.  To  find  the  range. 

With  the  assumed  value  of  gd  and  0  we  find  X^  by  the 
method  described  in  lb,  or  X^  =  11949      feet. 
Ave  also  have  X'  =  15045.4     '' 

Z  =  Z'-|-X,  =  26994.4     '' 

But  this  range  is  too  great  by  the  distance  B^C,  figure  14. 
To  find  this  distance  we  assume  that  this  short  arc  coincides 
with  its  tangent,  which  by  assumption  makes  an  angle  of  16° 
with  the  horizon, 


XX. — EXTERIOR    BALLISTICS.  37 


Therefore 


B'C  =  -i??^  =  477.4  ft.  and  X,  =  11471.6  ft. 
tan  16 

and  X  =  26517. 0  ft.  =  8839  yds.  =  5  miles  + . 

4.  To  find  the  incHnation  at  the  end  of  the  range  or  the 
angle  of  fall,  oo. 

We  can  vouch  for  only  the  elements  of  the  trajectory  in  the 
ascending  branch,  but  if  we  can  determine  the  range  as  by 
firing  or  by  the  method  just  described,  we  may  approximate 
closely  to  the  angle  of  fall. 

For 

V       tan  GD 
tan0  =  ^  =  — -; 

.  •.  tan  G?  =  V  and  Ce9  =  15°  20'  28". 
^/ 

In  the  example  this  gives  a  difference  of  but  6. 8  feet  in  the 
two  values  of  K,  which  difference  can  be  further  reduced  to 
0  by  successively  approximating  to  the  true  value  of  oj,  or 
G)  =  15°  18'  12" ;  and  therefore  ±^=7°  47'  |i  and  ~v,  == 
1323,  z7,  =  1067.3,  X,  =  3840  yds. 

These  values  will  be  hereafter  employed,  since  it  is  most 
important  to  have  a  correct  knowledge  of  the  elements  of  the 
trajectory  at  its  further  end. 

Practical  Methods  for  Detennining  w. 

1.  Fire  through  a  screen  near  the  point  of  fall,  and  note  the 

height  /if  of  the  hole  above  the  horizontal  plane  on  which 

the  projectile  strikes,  and  the  distance  of  its  impact,  d,  beyond 

/i 
the  screen.     Then  tan  w  =  -—  nearly. 


38  XX. — EXTERIOR     BALLISTICS. 


Or  note  the  inclination  of  the  shot-holes  in  snow  or  in 
horizontal  targets  composed  of  double  layers  of  boards. 

2.  Determine  the  range  OR,  figure  15,  for  a  given  value 
of  Q,  and  then  increase  ^  by  a  slight  increment  AB.  This 
will  increase  OR  by  AR  =  RR\ 

Then  assuming  HR'  to  be  straight  and  parallel  to  the  tan- 
gent at  R, 

.      RR      Rt^nAf) 
'^'''^  =  RR'  =  -AR~'''^'^y- 


3.  Determine  the  range  under  two  sets  of  conditions  differ- 
ing only  in  the  height,  /i,  of  the  gun  above  the  horizontal 
plane.     Then  if  this  difference  be  relatively  small  with  regard 

to  the  range  from  figure  16,  tan  go  =  --t-=  . 

4.  Figure  17  shows  how  this  would  practically  be  done, 
since  it  would  be  difficult  to  raise  a  gun  sufficiently  without 
displacing  it  horizontally  : 


tan  6)  = 


0'  R>  —  O  R. 


Application, 

Range-tables  are  constructed  to  give  all  the  principal  ele- 
ments of  the  piece,  charge,  and  trajectory  for  different  ranges.* 

The  following  method  and  figure  18  show  how,  having  a 
range-table,  we  may  determine  the  co-ordinates  of  the  vertex. 

Find  in  the  range-table  two  angles  of  departure  and  of  fall 
a  and  j3,  such  that  their  sum  =:  6.  Then  by  the  principle  of 
rigidity  S  will  be  the  chord  to  the  vertex,  and  S  cos  /?  =  X', 
and  5  sin  i3  -  Y'. 


*  See  Chapter  XXX,  pages  9,  52. 


XX. EXTERIOR,  BALLISTICS. 


5.  To  find  the  dangerous  space  at  any  range,  or  the  hori- 
zontal distance  over  which  a  target  of  given  height  would  be 
struck. 

We  have  in  this  case  to  find  the  distance  at  which  the  height 
of  the  trajectory  is  equal  to  that  of  the  target.  The  target  will 
evidently  be  struck  when  situated  at  this  point,  since  the  tra- 
jectory passes  through  its  summit,  and  it  will  also  be  struck 
if  situated  at  any  point  intermediate  between  this  and  the  end 
of  the  range.  Hence  if  D,  figure  8,  be  the  target  the  dan- 
gerous space  is  DR. 

The  simplest  way  of  determining  this  is  as  follows.  Sup- 
pose the  target  to  be  30  feet  high,  then  from  (HI") 

cr;.  =  O-1067  3  +  -T—r  =  40626. 4  +  31.9  =  40658. 3  =  (T^^^,^ ; 
sm  0 

or  z;,  =  1070.9. 
Similarly 

x  =  DS-  219. 2  ft.  =  73  yds. 

If  the  proper  value  of  w  has  been  found,  the  same  result 
may  be  obtained  by  working  downward  from  the  vertex,  tak- 
ing y  =  1576.1  —  30  r=  1546.1,  and 

Ovn  =  (^v. ■ — 7  =  CT  ,070  3  as  before.* 

sm  0 

The  accordance  of  these  methods  tests  the  accuracy  of  the 
determination  of  w ;  but  without  exacting  the  somewhat  labo- 
rious process  required  for  this  determination,  a  check  of  the 
accuracy  with  which  the  dangerous  space  has  been  determined 
may  be  had  by  observing  that  the  angle  whose  tangent  is 
equal  to  the  height  of  the  target  divided  by  the  dangerous 
space  is  greater  than  0  and  less  than  w. 


*  Or  taking  the  trial  values  assumed  for  the  descending  branch ,  viz^ 
Vy  =  1113 ; J/ ^  =  \S24.2'yV yy=z  1061  we  have  as  an  approximation 
^  =  1683 J  v'^^  =5 1064  ',xs=a  202.6  ft. 


40  XX. — EXTERIOR     BALLISTICS. 


The  dangerous  space  is  one  of  the  most  important  proper- 
ties of  a  trajectory,  since,  Chap.  I,  it  measures  the  chances  of 
striking  an  object  at  a  distance  which  in  warfare  is  only  ap- 
proximately known. 

The  flatter  the  trajectory  at  its  further  end  the  greater  is  the 
permissible  margin  of  error  in  estimating  the  range  before 
aiming. 

The  principles  of  Chap.  XVI  and  equation  (30)  illustrate 
the  importance  of  high  velocities  and  high  sectional  densities, 
since  if  one  projectile,  a,  figure  19,  having  less  sectional  den- 
sity than  another,  projectile  b,  be  projected  with  equal  ener- 
gies at  the  same  ranges,  although  the  trajectory  of  a  may  be 
flatter  than  that  of  b  at  the  start,  yet  near  the  target  the  D.S. 
of  b  will  be  greater  than  that  of  a,  if  the  target  lies  beyond  the 
intersection  of  the  two  trajectories. 

Although  the  method  above  described  is  generally  followed, 
and  is  best  suited  to  cases  where  w  is  accurately  known,  a 
simpler  and  probably  a  more  accurate  plan  is  hereafter  given, 
page  44. 

6.  To  find  the  time  of  flight  to  any  distance.  Take  the 
distance  as  1000  yards  =  3000  feet,  as  in  \b.  We  have  from 
equation  (II)  and  data  previously  computed 

/  =  (r^.  —  r^//)  ^  =  (ri803.9  —  ^1097)  ^  =  1-  '^^03  sec. 

7.  To  find  the  time  of  flight  for  the  whole  range. 

1st.  We  proceed  as  in  No.  3,  using  equation  II  and  the 
corrected  value  of  v^^  =  1067.3. 

T  =  (t;/  —  r;,//)  -  =  9.8432  sees, 
and  r,  =  (r;,  -  nj  i  =  9.8569 


r=r  +  T,      =19.7001. 


XX. — EXTERIOR    BALLISTICS.  41 


2d.   Or  we  may  pass  directly  to  the  point  of  fall,  as  follows: 
rr=(r;.-r7ji=  19.566, 


which  is  sufficiently  accurate  for  most  purposes. 

3d.   If  the  true  value  of  oo  or  v^^  is  not  determined,  we  may 

still  approximate  to  T^  by  finding  the  time  4  required  for  the 

projectile  to  pass  over  the  correction  of  the  range  determined 

477 
in  No.  3,  with  the  velocity  u^^  or  4  =  — — -  =  0.454  sec. 

jLUoU 

Therefore  having  with  the  assumed  value  of  cl?  =  16°  found 
T,  =  10.266,  its  corrected  value  is  9.812,  which  added  to  7" 
makes  T=  19.6552  sees. 

4th.  Or,  if  we  neglect  the  difference  in  time  of  passage 
over    (y, —  Y' )j  due   to    the    resistance   of  the   air,    since 

/,  =  \/?(n/k_  v'f),  we  obtain  4=  0.4186  and   T,  = 

^  g 
9.8474  which  is  a  closer   approximation   than   9.812,  since 

T,  >  T! 


Scholium. 
Equation  (23),  which  may  be  written 

cos  0  g 

or 

gj^    COS0  gj^      COS0 

shows  that,  although  for  the  descending  branch  the  mean 
value  of  V  is  less  than  that  for  the  ascending  branch,  the  in- 
crease in  the  value  of  0  shown  by  equation  (29),  and  the  con- 
sequent decrease  in  cos  (f>,  may  compensate  and  keep  the  ra- 


42  XX. —  EXTERIOR    BALLISTICS. 


tio  nearly  constant ;  so  that  as  far  as  iifue  only  is  concerned 
the  trajectory  may  be  supposed  to  be  in  vacuo. 

That  this  is  practically  so  appears  from  the  equality  of  T 
and  T,  in  the  above  problem  and  in  those  solved  by  other 
methods. 

Consequently,  and  particularly  for  small  values  of  A,  when 
the  vertical  component  of  the  velocity  is  so  small  that  it  may 
be  safely  neglected,  the  time  to  the  vertex  may  be  safely  taken 
as  half  the  whole  time  of  flight,  and  in  cases  of  necessity 
Equations  (6)  and  (7)  may  be  employed. 

For  example,  for  this  case,  which  is  certainly  an  extreme 
one,  if  we  substitute  the  value  oi  T  —  19.70  sec.  in  the  equa- 

tion  K  =  "-^we  obtain  for  Y  a  value    1561,  which  is  only 

15.2  feet  less  than  that  before  deduced.  When  the  value  of 
A  is  large,  the  equations  of  the  trajectory  in  vacuo  cannot  be 
indiscriminately  applied. 

Principle  of  the  Vertex. 

From  the  above  follows  this  important  conclusion  :  If  we 
represent  the  time  to  the  vertex  by  /^  (read  /  vertex),  the  ve- 
locity at  the  vertex  by  z^y^,  and  the  corresponding  time  function 

T 

by  r^,  then  /a  =  y. 

Then  we  have  from  equation  (II),  generalized  as  to  notation, 
Ct.  —  ^  — '^^LZLEul  ~  r  '  —  r . 


and 


XX. — EXTERIOR     BALLISTICS.       ^  43 

Or,  the  time  function  of  the  velocity  at  the  vertex  is  equal  to  the 
arithmetical  mean  of  the  time  functions  of  the  velocities  at  each 
end  of  the  arc. 

This,  which  may  be  termed  the  principle  of  the  vertex,  is  of 
great  value  in  approximate  solutions. 

If  we  know  the  time  interval  /  corresponding  to  two  veloci- 
ties, of  which  one  is  known,  then  the  time  function  of  the  ver- 
tex of  any  arc  may  be  determined  as  follows,  from  the  above 
and  Equation  (II) : 

Cl  ,   Ct  ,^^- 

r  A  =  r^'  -  Y  =  -^v"  +  y .  (37) 

8.  To  find  the  inclination  at  the  top  of  the  target,  which 
we  will  now  assume  to  be  a  rampart  30  ft.  high,  so  that  what 
was  before  the  dangerous  space  will  be  the  safe  space. 

From  equation  (I),  with  the  corrected  values  given,  page  37, 
we  have 

d=cos(l)iS--6-\l,=  -0°,  35674=  -  0°  21'  24".*= 


=  cos  0  IS 6-  \  77  = 


therefore0  =  a7-^  =  15°18'12'"-O°21'24"  =  14°56'48". 

Or,  working  down  from  the  vertex,  0  =  14°  57'.  The 
true  safe  space  will,  owing  to  the  increasing  curvature,  be 

30 

somewhat  less  than  ; .,  ,o  ^r^,  =  ^^^  ^t- 

tan  14    57 

The  difference  between  this  result  and  that  before  reached 
for  the  dangerous  space  shows  the  limitations  of  the  ordinary 
method,  and  is  probably  due  to  not  having  found  the  correct 
value  of  0  for  the  function  d,  as  explained  page  25  and  in 
the  Appendix. 


41  1 

*  =  cos  T  47'  ^2  (^1070. 9  —  ^1067. 3)  ^. 


44  XX. EXTERIOR    BALLISTICS. 

A  closer  approximation  to  the  dangerous  space  would 
probably  be  found  from  the  principle  of  the  vertex,  as  fol- 
lows: 

Assuming  the  rigidity  of  the  trajectory,  the  tangent  at  the 
vertex  of  any  elementary  arc  is  parallel  to  the  chord.  So  that, 
finding  the  inclination  0/^,  at  the  vertex  of  the  arc  in  rear  of  the 
target  the  dangerous  space  may  be  found,  since 

D.S.  =  height  of  target  X  cot  0/,. 

By  using  the  corrected  values  pages  37  and   39, 

r  -\-  T 

w         1070.  8       I  1067.  3 

we  find 

V^  =  1069.1,    (^,„,,.,  --(^,„,,.3  =  0°.0260, 

whence 

t/=  0°.1787  and  (p^  =15. 30 J  -  0.1787  =  15°  7',  47. 

D.S.  =  111  feet. 

This  method  enables  us  to  obtain  the  dangerous  space  quite 

closely  for  an  approximate  value  of  v^^ ,  and  to  determine  an 

important  element  without  requiring  the  tedious  correction 

mentioned,  page  37. 

Assuming  then  v^^  =  1061,  the  velocity  along  the  tangent  is, 
since  u^^  =  v^^  cos  (f)  =  v„  cos  w. 

V,^  cos  0 

^"^■^^^^  =  1^93, 

the  vertical  component  of  which  is  v,,  sin  w  =  1093  sin  16"  = 
301. 

The  time  of  passage  over  the  height  of  30  ft.  with  this  ve- 
locity will  be  /  =  0.09961  sec,  though  it  will  actually  be  a  trifle 

less,  and  --  =  0.0071. 

4 


XX. — EXTERIOR    BALLISTICS.  45 


Ct 

Now  since  r^  =  7^./  +  -  =  r,„,,  +  0. 0071  =  230. 2330, 

.-.  v,^  =:  1061.8. 

Also,  since  d  =  cos  0  (c^ioei.e  -  ^loei)^  =  0.0845, 

30 

d>.  =  16°  -  0.0845  =15°  54'.  9  and^ =  105  feet. 

^'^  tan  0 

This  is  much  nearer  the  true  value  than  the  result  given  by 
the  method  described  page  39. 

Very  nearly  the  result  arrived  at  by  the  method  above  de- 
scribed, viz.,  105  feet,  would  be  obtained  by  taking  for  the  time 

of  passage  /  =  \J g  \  v'1576.2  -  |/1546.2l  =  0.0947  sec. 

9.  Having  the  initial  velocity  and  the  value  of  C,  to  find 
the  angle  of  departure  necessary  to  attain  a  given  range,  and 
other  elements. 

The  conditions  of  this  problem,  which  is  a  frequent  one  in 
practice,  require  (page  6)  that  the  rigidity  of  the  trajectory  be 
assumed  and  that  the  principle  of  the  vertex  be  applied. 


Solution. 

1.  The  piece  is  supposed  to  be  fired  with  its  axis  horizontal, 
and  we  compute  the  elements  of  the  trajectory  as  if  it  were 
the  descending  branch  of  an  imaginary  trajectory. 

Then  we  revolve  the  trajectory  upward  until  the  chord 
becomes  horizontal.  By  the  principle  of  rigidity  S  is 
taken  =  X,  which,  to  test  the  accuracy  of  the  method,  we 
take  =  26517.24  feet,  as  previously  determined. 


-f^'"   m  THE        -)^^:*v 


c 


iiiTh& 


46  XX. — EXTERIOR     BALLISTICS. 

From  equation  (III)  we  have 

(Tj,^^  =  (Tv'  —  Cx,  or  v^^  =  1081. 
^rom  equation  (II) 

^A  =  i  (^,833  +  ^:o8i)  or  v^  =  1348. 
Then  from  equation  (I),  since  6  =  0  and  cos  0=1, 

d  =  1-:^A  =  11°  26'  13"  =  e. 

Compare  these  results  with  those  previously  deduced. 
2.   In  such  a  case,  to  determine  the  angle  of  fall  and  the 
dangerous  space,  we  would  proceed  as  follows  : 

Find  D,  in  degrees,  the  total  change  =  6  -\-  go,  hy  saying 

■^  =  (^:,3.  -  ^.08:)  ^=  26°.29  =  26°  17'  24"; 

then  a?  =  Z>  -  ^  =  14°  51'.  2  and 
SO 

It  is  evident  from  the  above,  that,  knowing  the  angle  of  fall 
required  to  strike  near  its  foot  a  scarp  protected  by  a  cover 
at  a  known  height  and  separated  from  it  by  a  ditch  of  known 
width,  it  is  only  necessary  to  know  the  distance  of  the  breach- 
ing battery  from  the  wall,  and  the  ballistic  coefficient  of  the 
projectile,  to  determine  approximately  the  value  of  6  and  of 
the  initial  velocity  or  charge  of  powder  required  to  strike  the 
wall  at  nearly  the  desired  spot,  with  a  required  remaining 
energy. 

It  was  by  some  such  method  that  the  German  artillery 
breached  at  hitherto  unknown  ranges  the  invisible  walls  of 
Strasburg.     See  problem  page  51. 


XX. — EXTERIOR    BALLISTICS.  4? 

Thus,  by  the  principle  of  rigidity, 

From  CX  =  ay  —  c^  determine  V  and  weight  of  charge. 

**      CD^Sy-  d^  *'        D. 

*'      conditions  **         go. 

**      D  —  GO  "6. 

MODIFIED   FORMULA. 

For  low  angles  of  departure  and  high  velocities  and  sec- 
tional densities  giving  small  values  of  A,  the  principle  of 
rigidity  permits  the  formulae  on  page  28  to  be  written 

Cd  •=  Sy  —  6^  ,  (A) 

a  =  Ty  —  T^;  (B) 

0=  ay  —  (7^,.  (C) 

In  these  formulae,  since  sin  0  =  0,  we  must  resort  to  Equa- 
tions (0)  and  (7)  as  explained  page  7,  or 

y=^(T-():  (6) 

y=^^  (7) 

The  propriety  of  this  assumption  appears  from  applying  it 
to  the  case  of  the  100-ton  gun,  assuming  the  velocities  to  be 
horizontal  and  solving  without  reference  to  the  vertex.  Thus, 
assuming  as  before  (o  =  16°,  we  have  from  (A),  using  whole 

numbers,  27°.83  =  (6,^  —  6„)  ~  .-.  2/,,  =1061. 

Similarly  we  find  T=  19.94  sec.  and  X  =  8983  yards,  lead- 
ing, as  seen  by  comparison,  to  but  slight  errors  providing  that 
0)  has  been  correctly  assumed. 

So  that  we  may  have  confidence  in  the  results  obtained  by 
the  use  of  Equations  (A),  (B),  (C),  when  v  does  not  differ 
much  from  u ,  and,  when  v  sin  (p  is  so  small  that  it  may  be 
neglected,  we  may  use  Equations  (6)  and  (7). 


48  XX. — EXTERIOR    BALLISTICS. 


Example. 

The  Springfield  rifle  and  ammunition  give  the  following 
data : 

W=  500  gr.  =  0.071428  lbs.  ; 

Diameter  of  projectile  =  0.455  inches  in  flight  • 

V=  1300  ft. 

By  experiment  we  find  that  for  a  range  of  500  yards  0  as 
measured  by  the  breech  sight  =  1°  17'  18". 

1.  Find  GO. 

1st.  From  (C)  determine  v^  =  869 

2d.      **      (A)         "  D  =  2°  40'  23". 

3d.       '*      D-d''  fi9  =  l°23'05". 

2.  Find  r. 

1st.  From  {B)  determine  T=  1.467  sec. 
2d.       "     (7)  ''         i"=8'.662  feet. 

3.  Findj^/  at  400  yards  =  1200  ft. 

1st.  From  (C)  determine  v  at  1200  ft.  -=  921. 
2d.       "     (B)         "  /  to  1200  ft.  =  1.132  sec. 

3d.       "      (6)  and  T  above  determine  7  =  6.105  ft. 
By   this   means  we  may  construct  a  drawing  of  the  tra- 
jectory. 
4    Find  the 'Dangerous  Space  at  500  yards. 
The  target  is  a  man  5  ft.  8  in.  (5§  ft.)  high  =  y.     The  gun 
is  supposed  to  be  fired  lying  down  (from  the  ground)  and  to 
be  aimed  at  the  feet  of  the  man. 

1st.  Reckoning  from  the  summit  of  the  trajectory  we  have 

^1  ^  y  "~      =  0.4313  for  the  time  from  the  vertex  to 

T 

the  top  of  the  man's  head,  and  -^  —  /,  =  time  over  D.  S.  = 

0.3022  =  f, 

2d    From  /'  and  (B)  determine  v  at  target  =  915. 
3d.  From  (C)  determine  D.  S.  =  267  ft.  =  89  yds. 


XX. — EXTERIOR  Ballistics.  49 

It  is  generally  1  etter  to  work  backward  from  the  point  of 
fall  than  forward  from  the  gun,  as  the  results  are  more  con- 
sistent if  the  data  are  supplied  from  only  one  branch  of  the 
trajectory.     See  page  39. 

However,  this  does  not  apply  in  the  above  case,  in  which 
the  vertical  resistance  of  the  air  is  wholly  neglected,  so  that 
the  same  results  would  follow  from  either  course  of  procedure. 
See  page  41. 

Alternate  Solution, 

If  in  Equation  (6)  we  supply  the  value  of  T  previously 
deduced,  and  solve  the  resulting  quadratic  equation,  we  shall 
have  two  values  of  /,  one  of  which  gives  the  time  for  the 
projectile  to  rise  to  the  height  of  j/,  and  the  other  which  gives 
the  time  for  the  projectile  to  rise  to  the  vertex  and  to  fall 
to  this  height  above  the  horizontal  plane,  so  that  there  will 
be  two  dangerous  spaces,  the  interval  between  them  being 
the  safe  space. 

It  is  evident  that  as  the  range  decreases,  the  other  conditions 
remaining  constant,  the  safe  space  finally  becomes  0.  The 
resulting  dangerous  space  will  then  be  continuous  and  a 
maximum. 

The  maximum  dangerous  space  for  a  given  small-arm  thus 
depends  upon  a  physical  constant, — the  height  of  a  man  ; 
and  assuming,  as  above,  the  mean  height  of  a  man  to  be  5f 
feet,  the  maximum  dangerous  space  will  be  a  function  of  p', 
page  23,  and  will  be  a  convenient  measure  of  the  joint  power 
of  the  gun  and  ammunition.      The  height  i^will  =  5f  feet. 

5.  Find  the  maximum  Dangerous  Space  for  the  preceding 
ballistic  condidons. 

Sec. 

1st.   From  (7)  determine  T=  1.187. 

2d.        ''      (B)         *'  z;=912 

3d.       ''      (C)         **         X=  416.6  +  yds.  =  max.  D.  S. 


50  XX. — EXTERIOR    BALLISTICS. 


APPENDIX   A. 

The  value  of  0  was  obtained  approximately  by  Mr.  Niven 
from  an  expanding  series.  (See  Proceedings  of  the  Royal 
Society  of  England,  1887;  No.  181.) 

The  value  of  0  to  be  used  with  Table  IV  for  changes  of 
inclination  is  that  given  in  the  text  for  high  angles  of  depart- 
ure, say  ^  >  5°. 

For  6*  <  5°  0  may  be  taken  =.  ^  ~l    -. 

For  the  other  tables  he  takes 

though,  where  greater  approximation  is  required,  for  changes 
of  time  he  uses 

APPENDIX   B. 

Problems. 

The  answers  given  below  result  from  the  use  of  the  modi- 
fied formulae. 

1.  The  3.2-inch  steel  b.  1.  rifle.  Weight  jof  shell  or  shrap- 
nel =  13  lbs.     I.  V.  =  1634. 

Determine  :  (1)  The  distance  at  which  v  of  shrapnel  will  be 
500. 

(2)  Time  of  flight  for  this  distance. 

(3)  Angle  of  departure  for  this  range,  supposing 

the  shrapnel  to  explode  40  ft.  above  the 
object,  or  the  angle  of  sight  —  y'. 
Answers  :  (1)  19,106  ft.  or  3.62  miles. 

(2)  24.6  sec. 

(3)  24'^  44'. 


XX. — EXTERIOR   BALLISTICS.  Bl 

2.  A  target  is  to  be  placed  on  Cro'  Nest.  The  distance 
from  the  sea-coast  battery  to  target  is  1990  yards ;  height  of 
target  above  battery  is  237  feet.  .  Determine  the  angle  of 
departure  necessary  to  strike  the  target,  using  the  8- inch  con- 
verted  rifle.       ,/ =  7.  95  inches  ; 

Weight  of  projectile  =  180  lbs. ; 

I.  V  =1414.  Answer:  5°  45'. 

3.  The  6-inch  b.  1.  rifle  requires  according  to  the  range 
table  an  elevation  of  1°  51'  and  a  muzzle  velocity  of  1850  f.  s. 
to  strike  an  object  at  a  distance  of  2U00  yards.  On  firing  the 
range  obtained  was  only  1800  yards,  and  investigation  showed 
that  the  powder  was  damp.*  What  additional  elevation  would 
be  necessary  for  a  range  of  2000  yards  ?      tV=  loo  lbs. 

Answer  :  0°  28'. 

4.  At  the  siege  of  Strasbourg  in  1870,  the  Germans  wished 
to  breach  the  scarp  wall  of  an  outwork  at  2000  yards  distance  ; 
the  ditch  was  known  to  be  50  feet  wide,  and  the  shell  were 
to  strike  12|-  feet  below  top  of  counterscarp  wall.  An  8-inch 
howitzer  firing  a  projectile  weighing  180  lbs.  with  a  muzzle 
velocity  of  700  f.  s.  was  employed. 

Required  the  striking  velocity  and  the  angle  of  departure 

A  i  616  f.  s. 

Answer  :  i 

(11°  47'. 

5.  At  a  range  of  1200  yards  a  64-lb.  shell  grazes  the  top  of 
a  traverse  8  feet  high.  How  far  beyond  the  traverse  will  the 
shot  strike  the  ground  ? 

^=6.171  inches; 

Weight  of  projectile  =  64  lbs. ; 

I.  V.  =  1260  f.  s. 

Answer  :  153  feet  or  51  yards. 

6.  A  Martini-Henry  rifle-bullet  strikes  a  vertical  target  at 
500  yards  at  a  certain  spot  when  the  muzzle  velocity  is  1353 
f.  s.      How  much  lower  on  the  target  will  the  same  projectile 

*See  proportion,  foot  p.  7. 


^2  XX. — EXTERIOR    BALLISTICS. 

Strike   if  the  muzzle  velocity  is  only  1300  f.  s.,  the  elevation 
and  other  conditions  remaining  the  same  ? 

^  =  0.45  inch. 

Weight  of  projectile  ==  480  grains  =  0.06857  lb. 

Answer  :  21|^  inches. 

7.  Using  the  Hebler  rifle,  determine  the  maximum  con- 
tinuous dangerous  space  for  a  man  kneeling. 

d  =0.296  inch; 
w  -  225  grains  =  0.03214  lb.; 
I.  V.  =1942f.  s.; 

Height  of  a  man  kneeling  =  42  inches. 
Compare  with  Springfield  rifle  : 
d  =0.45  inch  ; 
w  —  500  grains  =  0.07142  lb.; 
I.  V.  =  1316  f.  s. 

Answer:   Hebler  rifle,         458.0  yards. 
Springfiold  rifle,  340.7      '' 

8.  A  3-inch  Eureka  shell,  weight  9  lbs.,  fired  with  2  lbs.  of 
powder,  has  an  I.  V.  =  1495  f.  s.  With  what  charge  should 
a  10-lb.  shell  be  fired  to  have  at  407  yards  the  same  remain- 
ing velocity  that  the  full  charge  gives  at  2500  yards } 

Answer:  11.5  ounces. 

9.  A  3.2-inch  shell  weighing  13  lbs.  is  fired  with  a  muzzle 
velocity  =  958  f.  s.  The  target  is  at  a  distance  of  407  yards, 
and  the  angle  of  sight  is  4°  1'.  Determine  the  necessary 
breech-sight  elevation  and  the  quadrant  elevation. 

Answer:  e  =  V  19'. 
q  =  b°    20'. 

10.  A  3.2-inch  shell  weighing  13  lbs.  is  fired  with  I.  V.  i= 
986  f-  s.  How  high  above  the  gun  should  be  placed  a  hori- 
zontal bar  at  a  distance  of  80  feet,  so  that  the  shell  shall 
strike  the  bar  and  hit  a  target  on  the  same  level  as  the  gun, 
and  at  a  distance  of  1200  yards.  Determine  also  the  neces- 
sary breech-sight  elevation. 

Answer:  Height  =  4  ft.  6.5  ins. 
^  =  4°  0'  22'^ 


XX.— EXTERIOR  feALLlSTlCS. 


BALLISTIC   TABLES. 


Table  I. 

Value  of  K  for  the  Cubic  Law  of  Resistance,  Ogival-headed 
Projectiles  {1%,  diameter  heads). 


Velocity. 

Value 
ofK. 

Velocity. 

Value 
OfK. 

Velocity. 

Value 
OfK. 

Velocity. 

Value 
OfK, 

f.8. 

f.s. 

f.s. 

f.s. 

400  .... 

148 

0 

880  .... 

75 

0 

1360  . . . . 

106 

7 

1840  .... 

75 

2 

410  . . . . 

145 

2 

890  .... 

75 

0 

1370  . . . . 

106 

3 

1850  .... 

74 

7 

420  . . . . 

142 

5 

900  .... 

75 

0 

1380  .... 

105 

8 

1860  .... 

74 

2 

430  . . . . 

139 

8 

910  ..:. 

75 

0 

1390  . . . . 

105 

3 

1870  .... 

73 

6 

440  .... 

137 

2 

920  .... 

75 

0 

1400  . . . . 

104 

7 

1880  .... 

73 

1 

4r)0  . . . . 

134 

6 

930  .... 

75 

0 

1410  . . . . 

104 

1 

1890  .... 

72 

6 

460  .... 

132 

0 

940  .... 

75 

0 

1420  . . . . 

103 

5 

1900  .... 

72 

1 

470  . . . . 

129 

4 

950  .... 

75 

0 

1430  . . . . 

102 

9 

1910  .... 

71 

6 

480  .... 

126 

9 

960  .... 

75 

0 

1440  . . . . 

102 

3 

1920  .... 

71 

2 

490  ..  . 

124 

4 

970  .... 

75 

0 

1450  . . . . 

101 

6 

1930  .... 

70 

a 

500  . . . . 

121 

9 

980  .... 

75 

0 

1460  . . . . 

100 

9 

1940  .... 

70 

4 

510  . . . . 

119 

6 

990  .... 

75 

0 

1470  . . . . 

100 

1 

1950  .... 

70 

0 

520  . . . . 

117 

3 

1000  .... 

75 

0 

1480  .... 

99 

4 

1960  .... 

69 

7 

530  .... 

115 

0 

1010  .... 

75 

1 

1490  . . . . 

98 

6 

1970  .... 

69 

4 

540  . . . . 

112 

8 

1020  .... 

75 

3 

1500  . . . . 

97 

9 

1980  .... 

69 

2 

550  . . . . 

110 

7 

1030  .... 

76 

7 

1510  . . . . 

97 

1 

1990  .... 

69 

0 

5G0  . . . . 

108 

7 

1040  .... 

80 

8 

1.520  . . . . 

96 

2 

2000  .... 

68 

8 

570  . . . . 

106 

7 

1050  .... 

87 

3 

1530  . . . - 

95 

3 

2010  .... 

68 

6 

580  . . . . 

104 

6 

1060  .... 

94 

0 

1540  . . . . 

94 

4 

2020  .... 

68 

4 

530  . . . . 

102 

5 

1070  .... 

98 

7 

1550  . . . . 

93 

6 

2030  .... 

68 

3 

600  . . . . 

100 

5 

1080  .... 

102 

2 

1560  . . . . 

92 

8 

2040  .... 

68 

2 

610  . . . . 

98 

6 

1090  .... 

104 

9 

1570  

92 

0 

2050  .... 

68 

1 

620  .... 

96 

8 

1100  .... 

lOG 

9 

1580  .... 

91 

2 

2060  .... 

68 

0 

630  . . . . 

95 

1 

1110  .... 

108 

4 

1590  .... 

90 

4 

2070  .... 

67 

9 

640  . . . . 

93 

5 

1120  .... 

109 

2 

1600  .... 

89 

7 

2080  .... 

67 

9 

650  . . . . 

91 

9 

1130  .... 

109 

6 

1610  .... 

89 

0 

2090  .... 

67 

8 

660  . . . . 

90 

5 

1140  .... 

109 

6 

1620  .... 

88 

3 

2100  . . . 

67 

8 

670  . . . . 

89 

1 

1150  .... 

109 

6 

1630  . . . . 

87 

6 

2110  .... 

67 

7 

630  . . . . 

87 

7 

1160  ..  . 

109 

6 

1610  . . . . 

86 

9 

2120  .... 

67 

6 

69S  .... 

86 

3 

1170  .... 

109 

6 

1650  . . . . 

86 

2 

2130  .... 

67 

6 

700  .... 

84 

9 

1180  .... 

103 

6 

1660  . . . . 

85 

5 

2140  .... 

67 

5 

710  .  . . . 

83 

7 

1190  .... 

109 

6 

1670  . . . . 

84 

8 

2150  .... 

67 

4 

720  .... 

82 

6 

1200  .... 

109 

6 

1680  . . . . 

84 

2 

2160  .... 

67 

3 

730  . . . . 

81 

6 

1210  .... 

109 

6 

1690  . . . . 

83 

6 

2170  .... 

67 

2 

740  .... 

80 

6 

1220  .... 

109 

6 

1700  . . . . 

83 

0 

2180  .... 

67 

2 

750  .... 

79 

6 

1230  .... 

109 

5 

1710  . . . . 

82 

4 

2190  .... 

67 

1 

760  .... 

78 

7 

1240  . . . 

103 

5 

1720  .... 

81 

8 

2200  .... 

67 

0 

770  . . . . 

78 

0 

1250  .... 

109 

4 

1730  . . . . 

81 

2 

2210  .... 

66 

9 

780  .... 

77 

4 

12f30  .... 

103 

3 

1740  . . . . 

80 

6 

2220  ... 

66 

8 

790  ... 

76 

8 

1270  .... 

103 

2 

1750  .... 

80 

0 

2230  .... 

66 

8 

800  .... 

76 

2 

1280  .... 

103 

0 

1760  . . . . 

79 

5 

2240  .... 

66 

7 

810  . . . . 

75 

6 

1290  .... 

108 

8 

1770  .... 

78 

9 

22-0  .... 

66 

6 

820  .... 

75 

2 

1300  .... 

108 

6 

1780  .... 

78 

4 

2260  .... 

66 

5 

830  .... 

75 

1 

1310  .... 

lOS 

4 

1700  . . . . 

77 

8 

'  2270  .. 

66 

4 

840  . . . . 

75 

0 

1320  .... 

10^. 

1 

noo  .... 

77 

3 

,  2280  .... 

66 

2 

850  . . . . 

75 

0 

1330  .... 

107 

8 

1810  . . . . 

76 

8 

2290  ... 

65 

9 

860  . . . . 

75 

0 

1340  .... 

107 

5 

1820  . . . . 

76 

2 

2300  .... 

65-5 

870  . . . . 

75  0 

1350  .... 

1 

107  1 

[  1830  .... 

75-7 

u 


5C5t. — EXTERIOR  BALLISTICS. 


Table  II. 
Time  and  Velocity  Table,  Ct  =  r^,  —  r^„. 


V. 

0 

1 

2 

3 

4 

5 

6 

7 

8 

9 

Difl: 

f.8. 
40 
41 
42 

20  5-0299 
6-0554 
7  0276 

sees. 
5-1349 
6-1550 
7-1?,'^0 

sees. 
6-2393 
6-2540 
7-2159 

sees. 
5-3432 
6-3525 
7-3093 

sees. 

5-4466 
6-4505 
7-4022 

sees. 
5-5494 
6-5480 
7-4947 

sees. 
6-6517 
6  6450 
7-5867 

sees. 
5-7534 
6-7414 
7-0782 

sees. 

5  8546 

6  8373 
7-7693 

sees. 

6-9553 
6-93^7 
7-8599 

+ 

-1028 
-0975 
-0925 

43 
44 
45 

20  7-9501 
8-8272 
9-6622 

8-0398 
8  9125 
9-7435 

8-1291 
8-9974 
9-8244 

8-2179 
9-0819 
9-9050 

8-3063 
9-1660 
9-9852 

8-3942 
9-2497 
*0-0651 

8-4817 
9-3330 
*0  1446 

8-5687 

9  4159 

*0-2237 

8-6553 
9-4984 
*0-3025 

8-7415 
9-5805 
*0-3809 

-0879 
-0837 
•0799 

46 
47 

48 

21  0-4590 
1-2205 

1-9487 

0-5367 
1.2948 
2-0198 

0-6140 
1  3687 
2-0906 

0-6910 
1-4423 
2  1611 

0-7677 
1-5156 
2-2313 

0-8440 
1-5886 
2-3012 

0-9200 
1  6613 
2-3708 

0-9956 
1-7336 
2-4401 

1-0709 
1-8056 
2-5091 

11459 

1-8773 
2-5779 

-0763 
•0730 
-0699 

40 
60 
61 

21  2-6464 
3-3159 
3-9592 

2-7146 
3-3814 
4-0221 

2-7825 
3-4466 
4-0848 

2-8501 
3-5116 
4  1472 

2-9174 
3  5763 
4-2094 

2-9845 
3-6408 
4  2713 

3  0513 
3-7050 
4-3330 

3-1178 
3-7689 
4-3944 

3-1841 
3  8320 
4-4556 

3-2501 
3-8960 
4-5165 

-0671 
-0645 
-0619 

62 
63 
64 

21  4-5772 
5  1719 
5-7450 

4-6377 
5-2302 
5-8012 

4-6979 

5-2882 
5-8572 

4-7579 
5-3460 
5-9130 

4-8177 
5-4036 
5-9686 

4-8773 
5-4610 
6-0240 

4-9367 
5-5182 
6-0792 

4-9958 
5-5752 
6-1342 

5-0547 
5-6320 
6  1890 

6-1134 
5-6886 
6-2436 

-0596 
-0574 
-0554 

55 
66 
67 

21  6-2980 
6-8311 
7-3460 

6-3522 
6-8834 
7-3965 

6-4062 
6  9355 
7-4469 

6-4600 
6-9874 
7-49-71 

6-5136 
7-0391 
7-5471 

6-5670 
7  0907 
7-5970 

6-6202 
7-1421 
7  6467 

6-6732 
7-1933 
7-6962 

6-7260 
7-2444 
7  7456 

6-7786 
7-2953 
7  7948 

0534 
-0516 
•0499 

68 
69 
60 

21  7-8438 
8-3271 
8  7957 

7-8928 
8  3746 
8-8417 

7  9417 
8-4220 

8  8877 

7-9904 
8-4692 
8-9334 

8-0389 
8-5163 
8-9791 

8-0873 
8-5632 
9  0246 

8-1356 

8  6100 

9  0700 

8-1837 
8-6566 
9  1152 

8-2316 

8  7031 

9  1603 

8-2793 
8-7494 
9  2052 

-0483 
0468 
0454 

61 
62 
63 

21  9  2501 
9-6908 

22  0-1183 

9-2947 
9  7341 
0  1604 

9  3393 
9-7773 
0-2023 

9  3837 
9-8204 
0-2441 

9-4280 
9-8633 
0-2858 

9-4721 
9-9062 
0  3273 

9-5161 
9-9489 
0-3687 

9-5600 
9  9914 
0  4100 

9-6037 
*0-0338 
0  4512 

9  6473 

*0-0761 

0-4922 

-0441 
0428 
0415 

61 
65 
66 

22  0-5332 
0-9359 
1-3267 

0-5740 
0-9755 
1-3651 

0  6147 

1  0151 
1-4034 

0  6552 

1  0544 
1-4416 

0-6957 
1-0937 
1-4797 

0-7360 
1-1328 
1-5177 

0-7762 
1-1718 
1-5555 

0-8163 
1-2107 
1-5933 

0-8563 
1-2495 
1  6309 

0-8962 
1-2881 
1-6684 

-0403 
0391 
■0379 

67 
68 
69 

22  1-7059 
2  0742 
2-4322 

1-7432 
2  1105 
2-4675 

1-7804 
2  1466 
2-5027 

1  8175 
2-1827 
2-5377 

1-8545 
2-2186 
2-5727 

1-8914 
2-2545 
2-6076 

1-9281 
2-2902 
2-6424 

1-9648 

2-3259 
2-6771 

2-0014 
2-3614 
2  7117 

2-0378 
2-3969 
2-7462 

0368 
0358 
0348 

70 
71 

72 

22  2-7806 
3-1196 
3-4492 

2-8150 
3  1530 
3-4816 

2-8492 
3  1863 
3  5140 

2-8833 
3-2195 
3-5462 

2-9174 
3-2526 
3-5784 

2-9513 
3-2856 
3  6105 

2-9852 
3-3185 
3  6424 

3  0189 
3-3513 
3-6743 

3  0526 
3  3840 
3  7061 

3-0862 
3-4167 
3-7378 

0339 
-0330 
-0320 

73 
71 
75 

22  3  7694 
4  0804 
4-3828 

3-8009 
4-1110 
4  4125 

3-8323 
4  1416 
4-4422 

3-8636 
4  1720 
4-4719 

3-8949 
4-2024 
4-5014 

3-9260 
4-2326 
4-5308 

3-9571 

4-2628 
4-5602 

3-9881 
4-2929 
4-5895 

4-0189 
4  3230 
4  6187 

4-0497 
4-3529 
4-6478 

0311 
-0302 
-0294 

76 
77 
78 

22  4-6769 

1    4-9624 

5-2394 

4-7058 
4-9905 
6-2666 

4-7347 
5-0185 
5-2937 

4-7635 
5  0464 
5  3208 

4-7922 
5-0742 
5-3478 

4-8208 
5-1020 
5-3747 

4-8493 
5 ■ 129G 
5-4015 

4-8777 
5 • 1572 
5-4282 

4-9060 
5  1847 
5-4549 

4  9343 
5-2121 

5  4814 

-0286 
•0277 
-0268 

79 
80 
81 

22  5-5079 
5-7685 
6  0214 

5-5343 
5  7941 
6-0463 

5-5606 

5-8197 
6  0711 

5-5869 
5  -  8452 
6-0959 

5-6130 
5-8706 
6-1205 

6-6391 
5-8959 
6-1451 

5-6652 
5-9212 
6-1696 

5-6911 
5-9463 
6-1941 

5-7170 
5-9714 
6-2184 

5-7428 
5-9965 
6-2427 

-0261 
-0253 
-0245 

82 
83 
84 

22  6-2669 
6-5044 
6-7337 

6-2910 
6-5277 
6-7562 

6  3151 
6-5509 
6-7786 

6-3390 
6  5740 
6-8009 

6-3629 

6-5971 
6-8232 

6-3867 
6  6201 
6-8454 

6-4104 
6  6430 
6-8675 

6-4340 
6  6658 
6-8895 

6-4576 
6-6885 
6-9114 

6  4810 
6-7111 
6  9333 

0237 
0229 
-0221 

85 
86 

22  6-9551 

■7- 1688 
7-3752 

6-9768 

7-1898 
7-3954 

6-9984 

7-2107 
7  -U5G 

7  0200 

7  ■  2:315 
7-43J7 

7 -0415 

7-2522 
7-4358 

7-0629 
7-2729 

7-4757 

7 -0842 
7-2935 
7-4956 

7-1055 
7  3140 
7-5155 

7 -1267 
7-3345 
7  5353 

7-1478 
7-3549 

-0214 
-0206 
0199 

XX. — EXTERIOR   BALLISTICS. 


55 


Table  II. — Continued. 
Time  and  Velocity  Table,  Gt  —  r^, 


22  7 
7 
7 

22  8 


22  8 


22  9 
9 
9 

22  9 


22  9 

23  0 
0 

23  0 
0 
0 

23  0 
0 
0 

23  0 
0 
0 

23  0 
0 
0 

23  1 
•1 

1 

23  1 

1 
1 

23  1 

1 
1 

23  1 

1 
1 

23  1 
1 

1 


5746 
7677 
9544 

1346 
3090 
4778 

6411 
7994 
9528 

1014 
2454 
3851 

5207 
6522 
7796 

9024 
0177 
1226 

2170 
3031 
3835 

4593 
5314 


6668 
7311 


8545 
9142 
9720 

0283 
0832 
1367 


3381 
3855 
4318 

4771 
5214 
5647 

6071 
6486 
6893 


23  1  7291 
1-7682 
1-8066 


5942 
7866 
9727 

1523 
3261 
4943 

6572 
8150 
9678 

1160 
2596 


5340 
6651 
7921 

9144 
0287 
1325 


3114 
3913 

4667 
5384 
6071 

6733 

7374 
7997 

8605 
9200 
9777 

0338 
0886 
1420 

1941 
2449 
2945 

3429 
3902 
4364 

4816 
5257 
5690 

6113 
6527 
6933 

7331 
7721 
8104 


6137 
8055 


1699 
3432 
5109 

6732 
8305 


1306 

2737 
4126 

5473 
6780 
8046 

9262 
0396 
1423 


4740 
5454 
6139 

6798 
7437 
8059 

8665 
9259 


0394 
0940 
1473 

1992 
2499 
2994 

3477 
3948 
4410 

4860 
5301 
5732 

6155 
6568 


7370 
7760 
8142 


2347  0 
3196  0 
0 


6332 
8244 
0091 

1875 
3602 
5273 


8459 
9978 

1451 

2878 
4262 

5606 
6C08 
8170 


0504 
1520 

2435 
3278 
4067 

4813 
5524 
6206 

6863 
7500 
8120 

8726 
9317 


0449 
0934 
1525 


2549 
3043 

3524 
3995 
4455 

4905 
5345 
5775 

6196 
6609 
7013 

7410 

7798 
8179 


6526 
8431 
0272 

2050 
3772 
5437 

7051 
8613 
0128 

1595 
3018 
4398 

5738 
7036 
8294 

9496 
0610 
1615 

2522 
3359 
4143 

4885 
5593 


7563 
8181 

8787 
9375 
9947 

0504 

1048 
1578 


1-2095 
1-2599 
1  3091 


3572 
4041 
4501 

4949 
5388 
5818 


7449 
7837 
8217 


6719 


sees. 

7- 


0452  j  8 

2225  !  8 

3941  8 
5601 


7209 
8767 
0276 


1740  '  9 
3158  !  9 
4534  9 


7164 
8417 

9612 
071G  0 
1710  0 

0 
0 
0 

0 
0 
0 

0 
0 
0 

0 
0 

1 

1 
1 
1 

1 
1 
1 

1 

1 
1 

1 
1 
1 

1 
1 

1 

1 
1 
1 


3439 
4219 

4958 
5662 
6339 


7625 
8242 

8847 
9433 
0003 

0559 
1101 
1630 

2146 
2649 
3140 

3619 
4088 
4546 


7875 
8255 


6912 


0632 


4109 
5764 

7367 
8920 
0425 

1884 
3298 
4670 

6001 

7291 
8540 

9727 
0820 
1804 

2694 
3520 
4295 


5731 
6405 


7056 

7688 


9490 
0059 

0614 
1154 
1682 

2196 
2698 


4134 
4591 


5475 
5902 

6321 
6731 
7133 

7527 
7913 
8292 


7 

9 

9 

sees. 
7-7104 
7-8991 
8-0812 

sees. 
7  7295 
7  9176 
8-0990 

sees. 
7  7486 

7  9360 

8  1168 

8-2573 
8  4277 
8  5927 

8  2746 
8-4445 
8-6089 

8-2918 
8-4611 
8  6250 

8-7525 
8  9073 
9-0573 

8-7682 
8-9225 
9  0720 

8-7838 

8  9376 

9  0867 

9  2027 
9-3437 
9-4805 

9-2170 
9  3575 
9-4939 

9  2312 
9  3713 
9  5073 

9-6132 
9-7418 
9-8662 

9-6262 
9-7544 
9-8783 

9-6392 
9  7670 
9  8904 

9-9841 
0  0923 
0-1897 

9-9954 
0  1025 
0  1988 

*0  0066 
0  1126 
0-2079 

0-2780 
0  3599 
0  4370 

0-2864 
0-3678 
0-4445 

0  2948 
0  3757 
0  4519 

0-5101 
0  5800 
0  6471 

0-5172 
0-5868 
0  6537 

0-5243 
0  5936 
0  6603 

0-7120 
0  7750 
0-8364 

0-7184 
0  7812 
0  8424 

0-7248 
0-7874 
0-8484 

0-8965 
0-9648 
1-0115 

0  9024 
0  9605 
1-0171 

0  9083 

0  9663 

1  0227 

10669 
1-1208 
11734 

1  0723 
1-1261 
1  1786 

10778 
1-1314 
1-1838 

1-2247 
1-2748 
1  3237 

1-2298 
1  2797 
1-3285 

1-2348 
1-2847 
1  3333 

1  3714 
1-4180 
1-4636 

1-3761 
1  4226 
1-4681 

1-3808 
1-4272 
1-4726 

1-6082 
1-5518 
1-5945 

1-5126 
1-5561 
1-5987 

1  5170 
1  5604 
1-6029 

1-6362 
1-6772 
1-7173 

1  6404 
1-6812 
1  7212 

1  6445 
1-6852 
1  7252 

1  7566 
1-7952 
1  8330 

1  7605 
1-7990 
1-8367 

1-7644 
1-8028 
1-8405 

m 


X5t. — EXTERIOR    BALLISTICS. 


Table  II. — Continued. 
Time  and  Velocity  Table,  Ct  =  r 


23  1 

1 


23  2 
2 
2 


23  2 
2 
2 


23  2 
2 


23  2 
2 
2 


23  2 
2 
2 


23  2 
2 
2 


23  2 
2 

2 

23  2 
2 
2 


23  2 
2 
2 

23  2 


23  2 
2 
2 

23  2 


23  3 
3 
3 


23 


8442 
8812 
9175 

9532 
9883 
0228 

0569 
0904 
1234 


2197 

2509 
2818 
3123 

3424 
3722 
4016 

4308 

4597 
4882 

5165 
5444 
5721 

5994 
62G5 
6533 

6798 
7061 
7320 

7577 
7832 
8084 

8333 

8580 
8824 

9065 
9304 
9541 

9776 
0008 
0237 

0465 
0690 
0913 

1134 
1353 
1569 


•8479 
•8848 
•9211 

!•{ 
1^{ 
1  < 

•9567 
•9918 
•0263 

1^{ 
!•' 
2  ( 

0602 
•0937 
•1267 

2  ( 
2( 
2  ] 

•1591 
•1912 
•2228 

2  ] 
2  ] 
2  5 

•2540 
•2849 
•3153 

2-' 
2' 
2- 

•3454 
•3751 
•4046 

2- 
2- 
2 

•4337 
■4625 
•4911 

2- 

2- 
2- 

•5193 
•5472 
•5748 

2- 
2- 
2- 

•6022 
•6292 
•6560 

2- 
2- 
2 

•6825 
•7087 
7346 

2- 
2- 
2- 

•7603 

•7857 
•8109 

2 
2- 
2- 

•8358 
•8604 
•8848 

2 
2- 
2- 

•9089 
•9328 
•9565 

2- 
2- 
2- 

•9799 
J  0031 
5  0260 

2- 
3- 
3- 

r0488 
J  0713 
{•0935 

3 
3^ 
3- 

$1156 
$1375 
J  1591 

3 
3 
3- 

•8517 
•8885 
•9247 

•9602 
•9952 
•0297 


•0636 
•0970 
•1299 

•1624 
•1944 
•2260 

•2571 

■2879 


•3484 
•3781 
•4075 

•4366 
•4654 
•4939 

•5221 
•5500 
•5776 

•6049 
•6319 


•6851 
•7113 
•7372 

•7628 
•7882 
•8134 


•8629 
•8872 


•9113 
•9352 


•9822 
0054 


0510 
•0735 
■0958 

1178 
1396 
•1613 


8554 
8921 
9282 

9638 
9987 
0331 

0670 
1003 
1332 

1656 
1975 
2291 

2602 
2910 
3214 

3514 
3810 
4104 

4395 
4683 
4967 

5249 
5528 


6076 
6346 


6877 
7139 
7398 

7654 
7908 
8159 

8407 
8653 


2  9137 
2 

2  9612 

2-9845 

3  0077 
3  0306 

3  0533 
3  0757 


3  1200 
3  1418 
3  1634 


8591 
8958 
9318 

9673 
0022 
0365 

0703 
1036 
1364 

1688 
2007 
2322 

2633 
2940 
3244 

3543 
3840 
4133 

4424 
4711 
4996 

5277 
5555 
5831 


6373 
6640 


7165 
7423 

7679 
7933 
8184 

8432 
8678 
8921 

9161 
9399 
9635 


0100 
0329 

0555 
0780 
1002 

1222 
1440 
1656 


8628 
8994 
9354 

9708 
0056 
0399 

0737 
1069 
1397 

1720 
2039 
2354 

2664 
2971 
3274 

3573 
3869 
4162 

4453 
4740 
5024 

5305 

5583 
5858 

6130 
6400 
6666 


7191 
7449 

7705 
7958 
8209 

8457 
8702 


9185 
9423 
9659 

9892 
0123 
0351 

0578 
0802 
1024 

1244 
1461 
1677 


8665 
9030 


9743 
0091 
0433 

0770 
1102 
1430 

1752 
2071 
2385 

2695 
3001 
3304 


3899 
4192 

4481 
4768 
5052 

5333 
5611 


6157 
6426 


6956 
7217 

7475 

7730 
7983 
8234 

8481 
8726 


9209 
9447 
9682 

9915 
0146 
0374 

0600 
0824 
1045 

1266 
1483 
1698 


8702 
9067 
9425 

9778 
0125 
0467 


1135 
1462 

1784 
2102 
2416 

2726 
3032 


3928 
4221 

4510 

4797 
5080 

5361 
5638 
5913 

6184 
6453 
6719 

6982 
7243 
7500 

7756 
8008 
8258 

8506 

8751 


9470 
9705 

9938 
0169 
0397 

0623 
0847 
1068 

1287 
1505 
1720 


8738 
9103 
9461 

9813 
0160 
0501 


1168 
1494 

1816 
2134 
2447 

2757 
3062 


3958 
4250 

4539 

4825 
5108 


5666 
5940 

6211 
6480 
6745 

7008 
7268 
7526 

7781 
8034 
8283 

8531 

8775 
9017 

9257 
9494 
9729 

9961 
0192 
0420 

0645 
0869 
1090 

1309 
1526 
1741 


8775 
9139 


•9848 
0194 
0535 

0870 
1201 
1527 

1848 
2165 
2478 

2787 
3093 
3394 

3692 
3987 
4279 

4568 
4854 
5137 

5416 
5693 
5967 

6238 
6506 
6772 

7034 
7294 
7552 

7806 
8059 
8308 

8555 
8799 
9041 

•9281 
•9518 
•9752 


0215 
0442 

0668 
0891 
1112 


XX. — EXTERIOR    BALLISTICS. 


57 


Table  II. — Continued. 
Time  and  Velocity  Table,  Ct  =  r^,  —  r^„ 


V. 

0 

1 

2 

3 

4 

5 

6 

7 

8 

9 

Diff. 

f.R. 
184 

185 
18G 

sees. 
23  3  1784 
3  1997 
3  2207 

Bees. 
3  1805 
3-2018 
3-2228 

sees. 
3  ■  1827 
3  2039 
3-2249 

g 
3 
3 
3 

ecs. 
1848 
2060 
2270 

sees. 
3-1869 
3-2081 
3-2291 

s 
3 
3 
3 

eca. 

1891 
2102 
2312 

sees. 
3-1012 
3-2123 
3-2333 

sees. 

3  1033 
3-2144 
3-2353 

8 
3 
3 
3 

ecs. 
1954 
2165 
2374 

sees. 
3-1975 
3-2186 
3-2395 

+ 

•0021 
-C021 

0021 

187 
188 
139 

23  3  2416 
3-2623 
3-2828 

3-2437 
3-2643 
3-2848 

3  2457 
3-2664 
3-2869 

3 
3 
3 

2478 
2683 
2889 

3-2499 
3-2705 
3-2909 

3 

3 
3 

2520 

2726 
2930 

3  2540 
3-2746 
3-2950 

3-2561 
3  2767 
3-2970 

3 
3 
3 

2582 
2787 
2091 

3-2602 
3-2803 
3-3011 

-0021 
-0021 
0020 

100 
191 
102 

23  3-3031 
3-3233 
3-3432 

3-3051 
3-3253 
3-3452 

3-3072 
3-3273 
3  3472 

3 
3 
3 

3092 
3293 
3492 

3-3112 
3-3313 
3-3511 

3 
3 
3 

3132 

3333 
3531 

3-3152 
3-3353 
3-3551 

3-3172 
3  3372 
3-3571 

8 

3 
3 

3102 
3302 
3500 

3-3212 
3-3412 
3-3G10 

-0020 
-0020 
-0020 

193 
104 
105 

23  3-3630 
3-3825 
3  4019 

3-3649 
3  3845 
3  4038 

3-3669 
3-3864 
3-4057 

3 
3 
3 

3689 
3884 
4077 

3-3708 
3  3903 
3  4096 

3 
3 
3 

3728 
3922 
4115 

3-3747 
3-3942 
3  4134 

3-3767 
3-3061 
3  4153 

3 
3 
3 

3786 
3080 
4172 

3-3806 
3  4000 
3-4192 

-0020 
0019 
0019 

IOC 

107 
108 

23  3  4211 
3  4400 
3-4588 

3-4230 
3-4419 
3  4606 

3-4240 
3-4438 
3-4625 

3 
3 
3 

4268 
4457 
4644 

3-4287 
3  4476 
3-4662 

3 
3 
3 

4306 
4494 
4681 

3-4325 
3-4513 
3-4699 

3  4344 
3-4532 
3-4718 

3 
3 
3 

4362 
4550 
4736 

8-4381 
3-45C9 
3-4755 

0019 
0019 
0019 

100 
200 
201 

23  3  4773 
3-4956 
3-5137 

3  4791 
3-4074 
3  5155 

3-4810 
3-4002 
3-5172 

3 
3 
3 

4828 
5010 
5190 

3-4846 
3-5028 
3  5208 

3 
3 
3 

4865 
5047 
5226 

3-4883 
3-5065 
3  5244 

3-4901 
8-5083 
3-5262 

3 
3 
3 

4920 
5101 
5280 

3-4938 
3-5119 
3-5297 

-0018 
0018 
0018 

202 

203 
204 

23  3-5315 
3-5402 
3-5666 

3-5333 
3-5500 
3-5683 

3-5351 
3-5527 
3-5700 

3 
3 
3 

5368 
5544 
5717 

3-5386 
3-5561 
3  5735 

3 
3 
3 

5404 
5579 
5752 

3-5421 
3-5596 
3-5769 

3-5439 
3-5614 
3-5786 

3 
3 
3 

5456 
5631 
5803 

8-5474 
3-5648 
3  5820 

0018 
•0017 
0017 

205 
208 
207 

23  3-5837 
3  6007 
3-6174 

3-5854 
3-6024 
3  6191 

3-5871 
3-6040 
3-6207 

3 
3 
3 

5888 
6057 
6224 

3  5905 
3-6074 
3  6240 

3 
3 
3 

5922 
6091 
6257 

3-5939 
3-6107 
3-6273 

3  5956 
3-6124 
3-6290 

8 
3 
3 

5973 
6141 
6306 

3-5990 
3-6157 
3  6323 

0017 
-0017 
-0016 

203 

2O0 
210 

23  3  6339 
3  6502 
3-6662 

3-6355 

3-6518 
3 -6078 

3-6372 
3-6534 
3-6694 

3 
3 
3 

6388 
6550 
6710 

3  6404 
3-6566 
3-6726 

3 
3 
3 

6420 
6582 
6741 

3-6437 
3-6598 
3-6757 

3-6453 
3-6614 
3-6773 

3 

3 
3 

6469 
6630 
6789 

8  6485 
3-6646 
3  6805 

-0016 
0016 
0016 

211 

212 
213 

23  3-6820 
3-6977 
3-7131 

3  6836 
3-6902 
3-7146 

3-6852 
3-7008 
3-7162 

3 
3 
3 

6867 
7023 
7177 

3-6883 
3-7039 
3-7192 

3 
3 
3 

6899 
7054 
7207 

3-6914 
3  7070 
3  7223 

3-6930 

3-7085 
3-7238 

3 
3 
3 

6946 
7100 
7253 

8-6961 
3-7116 
3-7268 

0016 
•0015 
0015 

214 
215 
216 

23  3-7283 
3-7434 
3-7582 

3-7298 
3  7448 
3-7597 

3  7313 

3 -7463 
3  7612 

3 
3 
3 

7329 

7478 
7626 

3  7344 
3-7493 
3  7641 

3 
3 
3 

7359 
7508 
7656 

3-7374 
3-7523 
3  7670 

3-7389 
3-7538 
3-7685 

3 
3 
3 

7404 

7552 
7700 

3-7419 
3-7567 
3-7714 

0015 
0015 
-0015 

217 
218 
210 

23  3  7729 
3-7874 
3-8016 

3  7743 

3  7888 
3  8031 

3-7758 
3  7002 
3  8045 

3 
3 
3 

7772 
7917 
8059 

3-7787 
3-7931 
3  8073 

3 
3 
3 

7801 
7945 
8087 

3-7816 
3-79G0 
3-8101 

3-7830 
3-7974 
3  8115 

3 
3 
3 

7845 
7988 
8129 

3-7859 
3  8002 
3-8144 

0014 
OOU 
0014 

220 
221 
222 

23  3-8158 
3-8297 
3  8435 

3-8372 
3  8311 
3  8448 

3  8186 
3-8325 
3  8462 

3 
3 
3 

8200 

8338 
8476 

8-8214 
3  8352 
3  8489 

3 
3 
3 

8227 
8366 
8503 

3-8241 
3-8380 
3  8517 

3-8255 
3  8394 
3  8530 

3 
3 

8269 
8407 
8544 

8  8283 
3-8421 
3-8557 

0014 
0014 
0014 

223 
224 

225 

23  3-8571 
3-8705 

3-8838 

3-8584 
3-8718 
3-8851 

3  8508 
3-8732 
3-8864 

3 
3 
3 

8611 
8745 
8877 

3-8625 
3-8758 
3-8890 

3 
3 
3 

8638 
8772 
8903 

3-8651 

3-8785 
3  8916 

3-8665 
3-8798 
3-8930 

3 
3 
3 

8678 
8811 
8943 

8-8692 
3  8824 
3-8956 

i  ooia 

0013 
-0013 

226 
227 
228 

23  3  8969 
3  00'^« 
3-922G 

3-8982 
3-9111 
3  92u9 

3-8995 
3  9124 
3-9252 

3 
3 

3 

-9008 
-9137 
9264 

3-9021 
3-9150 

3-9277 

3 
3 

3 

9034 
9162 
9290 

3-9047 
3-9175 
3  y..03 

3-9059 
3-91R8 
3  9315 

3 
3 
3 

9072 
9201 
-9323 

3-9085 
3-9214 
3  9341 

001& 
0013 
•0013 

229 
230 

23  3-9353 
3  9470 

3-9366 
3-9i92 

3-937S 

3- 0:01 

3 

-9301 
-9517 

3  9401 
3 -2029 

3 

9*15 

'  3-9429 
3-9554 

3-9441 
3-9507 

8 
3 

-9454 
9579 

3-9467 
3-9592 

0013 
0013 

58 


XX. EXTERIOR    BALLISTICS. 


Table  III 

Distance  and  Velocity  Table,  Cs  =  c^  —  (7^/,. 


feet. 

2  5008 

5424 

5827 


2  6219 
6601 
6972 

2  7335 
7688 
8034 

2  8373 
8704 
9029 

2  9347 
9659 
9966 

3  0267 
0.563 

.  0854 

3  1140 
1423 
1701 

3  1076 

2247 

-   2514 

3  2777 
3037 
3292 

3  3544 
3793 
4038 

3  4280 
4519 
4754 

3  4986 
5215 
5440 

3  5662 
5S80 
6094 

3  6305 
6512 
6716 

3  6916 
7111 
7303 

3  74nO 

7672 
7850 


feet. 
5050  2 
5464-9 
5867-3 


6258 
6638 
7009 

7370 
7723 
8068 

8406 
8737 
9061 


9690 


0297 
0592 


1169 
1451 
1729 


7 

2274 
2540  8 


3318 

3569 
3818 
4062 

4304 
4543 

4777 

5009 
5237 
5462 

5684 
5902 
6116 

6326 
6533 


7 
5 

1 
0 
1 

4 
1 
6736  3 

6935  7 
7131  0 
7322  0 

7^0'^ -5 
7690-5 
7868-2 


feet. 
5092 
5505 
5903 


6296 
6676 
7046 

7406 
7758 
8103 

8439 
8769 
9093 

9410 
9721 
0027 

0327 
0622 
0912 

1197 
1479 
1757 

2031 
2301 

2567 

2829 
3038 
3343 

3594 

3842 
4087 

4328 
4566 
4801 

5032 
52G0 
5484 

5706 
5923 
6137 

6347 
6553 
6756 

6955 
7150 
7340 

7526 
7708 
7885 


feet. 
5134 
5546 
5946 


6335 
6713 
7082 

7442 
7793 
8137 

8473 
8802 
9125 

9441 
9752 
^0057 

0357 
0651 
0940 

1226 
1507 

1784 

2058 
2327 


2855 
3114 


3619 
3867 
4111 

4352 
4590 


5055 
5282 
5507 

5728 
5945 
6158 

6368 
6574 
6776 

6975 
7169 
7359 

7.^45 
7726 
7903 


feet. 

5176 
5586 
5985 


'  6373 
6751 

I  7118 

I 

:  7477 
7828 

1  8170 


8835 
9157 


6  9472 

2  9783 

3  *0087 


0386 
0680 


9  ,   0969 


1254 
1535 
1812 


2354 
2020 

28S1 
3139 
3394 

3644 
3891 
4135 

4376 
4613 

4847 

5078 
5305 
5529 

5749 
5966 
6179 


6594 
6796 

6994 

7188 
7378 


3  7563 

4  7744 
3  '  7920 

I 


feet. 

5217 
5627 
6025 


6411 

6788 
7155 

7513 
7862 
8204 

8539 

8867 
9189 

9504 
9813 
mi7 

0416 
0709 
0998 

1282 
1563 
1839 

2112 

2381 
2646 

2907 
3165 
3419 

3669 
3916 
4159 

4400 
4637 
4871 

5101 

5328 
5551 

5771 
5988 
6200 

6409 
6614 
6816 

7014 
7207 
7397 

7581 
7762 
7938 


feet. 

5259 
5667 
6064 


6449 
6825 
7191 

7548 
7897 


8572 
8900 
9220 

9535 
9844 
"^0147 

0445 
0738 
1026 

1310 
1590 

1867 

2139 
2407 
2672 

2933 
3191 
3444 

3694 
3940 
4184 

4424 
4660 
4894 

5124 
5350 
5573 

5793 
6009 
6221 

6430 
6635 


7033 
7227 
7415 

7600 
7779 
7955 


feet. 

5300 
5707 
6103 


6487 
6862 
7227 

7583 
7931 
8272 


8932 
9252 

9566 
9874 
'^0177 

0475 
0767 
1055 

1339 

1618 
1894 

2166 
2434 


2959 
3216 
3469 

3719 
3965 
4208 


5815 
6030 
6242 

64.50 
6655 
6856 

7053 

7246 
7434 

7618 
7797 
7973 


4448 -0 
4684-4 

4917-4 

5146  9 
5373  0 
5595 


feet. 
5341 
5747 
6142 

6525 
6899 
7263 


7618 
7966 
8305 


8964 
9284 

9597 
9905 
'0207 

0504 
0796 


1367 
1646 
1921 

2193 
2461 
2725 


2985-4 
3242  0 
3494  7 

3743 
3989 
4232 


4471 
4707 
4940 

5169 
5395 
5617 

5837 
6052 
6263 

6471 

6675 
6876 

7072 

7265 
7453 

7636 
7815 
7990 


feet. 

5383  0 
5787  8 
6181  0 

6563-6 
6936  1 
7299-2 

7653-9 


8000 


8671 
8996 
9315 

9628 
9935 
^0237 

0534 
0825 
1112 

1395 

1674 
1949 

2220 
2487 
2751 

3011 

3267 
3519 

3768 
4014 
4256 

4495 
4731 
4963 

,  5192 

!  5417 

5640 


5858-7 
6073-6 
6284  6 

6492 


7092 

7284 
7471 

76.54 
7833 
8007 


XX — EXTERIOR    BALLISTICS. 


Table  III. — Continued. 
Distance  and  Velocity  Table,  Cs  =  o-^,  —  cr^,,. 


V. 

0 

1 

2 

3 

4 

6 

6 

7 

8 

9 

Dim 

88 
89 
90 

feet. 
3  8024-8 
8195  0 
8361-5 

feet. 
8042  0 
8211-9 
8377-9 

feet. 

8059  2 
8228-6 
8394-3 

feet. 
8076.3 
8245  4 
8410-7 

feet. 
8093-4 
8262-1 
8427-0 

feet. 
8110-4 
8278-7 
8443-3 

feet. 

8127-4 
8295-4 
8459-6 

feet. 
8144-4 
8312-0 
8475-8 

feet. 
8161  3 
8328-5 
8492-0 

feet. 
8178-2 
8345-0 
8508-2 

+ 

17-0 
16  6 
16-3 

91 
92 
93 

3  8524-3 
8683-5 
8839-4 

8540  4 
8699-3 
8854-8 

8556-4 
8715-0 
8870-2 

8572-4 
8730-7 
8885-5 

8588-4 
8746-3 
8900-8 

8604-3 
8761-9 
8916-1 

8620-3 
8777-5 
8931-3 

8636-1 
8793-0 
8946-5 

8652-0 
8808-5 
8961-7 

8667-8 
8824-0 
8976-8 

15  9 
15-6 
15  3 

94 
95 
96 

3  8991-9 
9141  2 
9287  4 

9007-0 
9156  0 
9301-9 

9022-0 
9170-7 
9316  3 

9037-0 
9185-4 
9330-7 

9052-0 
9200  1 
9345  0 

9066-9 
9214-7 
9359-4 

9081-9 
9229-3 
9373-7 

9096-7 
9243-9 
9387-9 

9111-6 
9258  4 
9402-2 

9126-4 
9272-9 
9416-4 

15  0 
14-6 
14-3 

97 
98 
99 

3  9430  6 
9570  8 
9708-3 

9444-7 
9584-7 
9721-9 

9458  9 
9598-6 
9735-4 

9473-0 
9612-4 
9749-0 

9487-0 
9626  1 
9762-5 

9.501-1 
9639-9 
9775-9 

9.515-1 
96.53-6 
9789-4 

9529  1 
9667-3 
9802-8 

9543-0 
9681-0 
9816-2 

9557-0 
9604-6 
9829-6 

14  0 
13-7 
13-5 

100 
101 
102 

3  9842  9 
9975  0 

4  0104  3 

9856  3 
9988  1 
0117  1 

9869-6 
*0001-1 
0129  8 

9882-9 
*()014-1 
0142-5 

9896-1 
*0027-l 
0155-2 

9909-3 

:*0040-0 

0167-8 

9922-5 
*00.52-9 
0180-4 

9935-3 

*0065-8 
0192  9 

9948  8 
*0078-7 
0-205  4 

9961-9 
*009l-5 
0217-8 

13-2 
12-9 
12-6 

103 
104 
105 

4  0230-1 
0349  4 
0459-2 

0242  4 
0360-8 
0469  6 

0254-6 
0372-2 
0479-9 

0266-8 
0383-4 
0490-0 

0278-8 
0394-5 
0500-1 

0290-8 
0405-6 
0510  1 

0302-7 
0416-5 
0520  0 

0314  5 
0427-3 
0529-8 

0326-2 
0438-1 
0539  5 

0337-8 
0448-7 
0549-2 

11  9 
11-0 
9-9 

106 
107 
108 

4  0558  7 
0650  5 
0736-8 

0568-2 
0659-3 
0745  2 

0577  6 
0668  1 
0753  6 

0.586-9 
0676-9 
0761-9 

0596  2 
0685-6 
0770-2 

0605-4 
0G94-2 
0778-4 

0614-5 
0702-8 
0786-6 

0623-6 
0711-4 
0794-8 

0632-6 
0719-9 
0802-9 

0641-6 
0728-4 
0811-0 

9  2 
8  6 
8-2 

109  ' 

110 

111 

4  0819  0 
0897-9 
0974-2 

0827-1 
0905  7 
0981  6 

0835  0 
0913-4 
0989  1 

0843-0 
0921-1 
0996  6 

0850-9 
0928-7 
1004-0 

0858-9 
0936-4 
1011-4 

0866-7 
0944-0 
1018-8 

0874-6 
09.51-5 
1026  2 

0882-4 
0959  1 
1033-5 

089(r 
0966 
1040 

2 
6 
9 

7-9 

7-6 

7-4 

112 
113 
lU 

4  1048  2 
1120  5 
1191  4 

1055-5 
1127-6 
1198-4 

1062-8 
1134-8 
1205-4 

1070  0 
1141  9 
1212  4 

1077-3 
1149-0 
1219-4 

1084-5 
1156-1 
1226-4 

1091-7 
1163  2 
1233  3 

1099  0 
1170  2 
1240  3 

1106-1 
1177-3 
1247-2 

1113 
1184 
1254 

3 

4 

1 

7-2 
71 
6  9 

115 
116 

117  1 

4  1261  0 
1329-5 
1396  8 

1267-9 
1336  3 
1403-5 

1274-8 
1343-1 
1410  1 

1281-7 
1349  8 
1416-8 

1288-6 
1356  6 
1423-4 

1295-4 
1363-3 
1430  0 

1302-3 
1370  0 
1436-6 

1309  1 
1376-7 
1443-2 

1315-9 

1383-4 
1449-8 

1322 
1390 
1456 

7 
1 
4 

6  8 
6  7 
66 

118 
119  i 
120 

4  1462  9 
1528-0 
1591  9 

1469  5 
1534-4 
1598-3 

1476-0 
1540  9 
1604-6 

1482  6 
1547-3 
1610-9 

1489-1 
1553-7 
1617-2 

1495-6 
1.560-1 
1623-5 

1502  1 
1566-5 
1629-8 

1508  6 
1572-9 
1636-1 

1515-1 
1,579-2 
1642-3 

1521 
1585 
1648 

5 
6 
6 

6  5 
6-4 
6  3 

121 
122 
123 

4  1654-8 
1716  7 
1777-5 

1661  1 

1722-8 
1783  6 

l«67-3 
1728-8 
1789-6 

1673-5 
1735  0 
1795-6 

1679-7 
1741  1 
1801  6 

1685-9 

1747-2 
1807-6 

1692-1 
1753  3 
1813-6 

1698-2 
1759-4 
1819-6 

1704-4 
1765  4 
1825  6 

1710 

1771 
1831 

5 
5 
5 

6-2 
6-1 
6  0 

124 

125  1 
126 

4  1837  5 
1896  5 
1954-6 

1843  4 
1902  3 
1960  4 

1849-4 
1908-2 
1966-1 

1855-3 
1914  0 
1971-9 

1861-2 
1919-8 
1977  6 

1867-1 
1925-6 
1983  3 

1873-0 
1931-5 
1989-0 

1878-9 
1937-3 
1994-8 

1884-8 
1943  0 
2000  5 

1890 
1948 
2006 

6 
8 
2 

5  9 

5  8 

5-7 

127 
128 
129 

4  2011-8 
2068-3 
21-23-9 

2017-5 
2073-9 
2129-4 

2023-2 
2079  5 
2135  0 

2028-9 
2085-0 
2140  5 

2034-5 
2090-6 
2146-0 

2040-2 
2096-2 
2151-5 

2045-8 
2101  8 
2157-0 

2051-4 
2107-3 
2162-4 

2057  0 
2112-9 
2167-9 

2062 
2118 
2173 

7 
4 
4 

5-6 
5-6 
5-5 

130 
131 
132 

4  2178-8 
2233  0 
2286  4 

2184-3 
2238-4 
2291-8 

2189-7 
2243-7 
2297-1 

2195-1 
2249-1 
2302-4 

2200-6 
2254-5 
2307-6 

2206  0 

22.59-8 
2312  9 

2211-4 
2265-1 
2318-2 

2216-8 
2270-5 
2323  5 

2222-2 
2275-8 
2328-7 

2227 
2281 
2334 

6 
1 
0 

5-4 
5  3 
53 

133 
134 
135 

4  2339-2 
2391-4 
2443  0 

2344-5 
2396  6 
2448-1 

2349-7 
2401  8 
2453-2 

2355  0 
2406  9 
2458-3 

2360  2 
2412  1 
2463  4 

2365-4 
2417-3 
2468-5 

2370-6 
2422-4 
2473-6 

2375-8 
2427-6 
2478-7 

2381-0 
2432-7 
2483-8 

2386 
2437 
2488 

2 
8 
9 

6-2 
5-2 
5-1 

60 


XX. — EXTERIOR    BALLISTICS. 


Table  III. — Continued. 
Distance  and  Yelocity  Table,  Gs  =  cr^, 


V. 

0 

1 

2 

3 

4 

5 

6 

7 

8 

9 

Diff. 

f.s. 
136 
137 
138 

feet. 
4  2493-9 
2544  4 
2594-3 

feet. 
2499  0 
2549-4 
2599-2 

feet. 
2504  1 
2554-4 
2604-2 

feet. 
2509-1 
2559-4 
2609  1 

feet. 
2514-2 
2564-4 
2614-1 

feet. 

2519-2 
2569-4 
2619  0 

feet 
2524- 
2574- 
2624- 

3 

4 
0 

feet. 
2529-3 
2579  4 
2628-9 

feet. 
2534-3 
2584-3 
2633-8 

feet. 
2539-4 
2589-3 
2638-8 

+ 
5  0 
5  0 
4  9 

139 
110 
141 

4  2643-7 
2692-6 
2741-2 

2648-6 
2697-5 
2746-0 

2653-5 
2702-4 
2750-8 

2658-4 
2707-2 
2755-7 

2663-3 
2712-1 
2760-5 

2668-2 
2717  0 
2765-3 

2673 

2721 
2770 

1 
8 
1 

2678-0 
2726-7 
2774-9 

2682-9 
2731-5 
2779-7 

2687-8 
2736-3 
2784-5 

4-9 
4-9 
4-8 

142 
143 
144 

4  2789-3 
2837-1 
2884-4 

2794  1 
2841-8 
2889  1 

2798-9 
2846-6 
2893-8 

2803-7 
2851-3 
2898-6 

2808-5 
2856-0 
2903-3 

2813-2 
2860-8 
2908-0 

2818 
2865 
2912 

0 

5 

7 

2822-8 
2870-2 
2917-4 

2827-5 
2875-0 
2922-1 

2832-3 
2879-7 
2926-7 

4-8 

4-7 
4-7 

145 
146 
147 

4  2931-4 
2978-1 
3024-5 

2936  1 
2982-8 
3029  1 

2940-8 
2987-4 
3033-7 

2945-5 
2992-1 
3038-4 

2950  1 

2996-7 
3043-0 

2954-8 
3001-3 
3047  6 

2959 
3006 
3052 

5 
0 
2 

2964-1 
3010-6 
3056-8 

2968-8 
3015-2 
3061-4 

2973-5 
3019-9 
3066-0 

4  7 
4  6 
4-6 

148 
149 
150 

4  3070-6 
3116  4 
3162-0 

3075-2 
3121  0 
3166  5 

3079  8 
3125-6 
3171  0 

3084-4 
3130  1 
3175  6 

3089  0 
3134-7 
3180  1 

3093-5 
3139-2 
8184-6 

3098 
3143 
3189 

1 
8 
2 

3102-7 
3148-3 
3193-7 

3107-3 
3152-9 
3198-2 

3111-8 
3157-4 
3202-7 

4-6 
4  6 

4-5 

151 
152 
153 

i  3207  2 
3252  3 
3297-2 

3211 • 8 
3256-8 
3301-7 

3216-3 
3261-3 
3306-2 

3220-8 
3265-8 
3310-6 

3225-3 
3270-3 
3315  1 

3229-8 
3274-8 
3319-6 

3234 
3279 
3324 

3 
3 
1 

3238-8 
3283-8 
3328-5 

3243-3 
3288-3 
3333-0 

3247-8 
3292-8 
3337-5 

4-5 
4  5 
4  5 

154 
155 
156 

4  3342-0 
3386-5 
3430  9 

3346-4 
3391-0 
3435-3 

3350  9 
3395-4 
3439-8 

3355-3 
3399-9 
3444-2 

3359-8 
3404  3 
3448-6 

3364-3 
3408-7 
3453  0 

3368 
3413 
3457 

7 
2 
4 

3373-2 
3417-6 
3461-9 

3377  6 
3422  0 
3466-3 

3382-1 
3426-5 
3470-7 

4-5 

4-4 
4-4 

157 
158 
159 

4  3475-1 
3519-1 
3563-0 

3479-5 
3523-5 
3567-3 

3483-9 
3527-9 
3571-7 

3488-3 
3532  3 
3576-1 

3492-7 
3536-7 
3580-4 

3497  1 
3541  1 
3584-8 

3501 
3545 
3589 

5 
4 
1 

3505-9 
3549-8 
3593-5 

3510  3 
3554  2 
3597-9 

3514-7 
3558-6 
3602  2 

4-4 
4-4 
4-4 

160 

161 
162 

4  3606  6 
3650-0 
3693-3 

3610-9 
3654-3 
3697  6 

3615-3 
3G58-7 
3701-9 

3619-6 
3663  0 
3706-1 

3624-0 
3667-3 
3710-5 

3628-3 
3671-6 
3714  8 

3632 
3676 
3719 

6 
0 

1 

3637  0 
3680-3 
3723-4 

3641-3 
3684-6 
3727-7 

3645-7 
3688-9 
3732-0 

4-3 
4-3 
4-3 

163 
164 
165 

4  3736-3 
3779-2 
3821-9 

3740-6 
3783-5 
3826-2 

3744-9 
3787-8 
3830-4 

3749  2 
3792  0 
3834-7 

3753-5 
3796-3 
3838-9 

3757-8 
3800-6 
3843-2 

3762 
3804 
3847 

1 
9 
4 

3766-4 
3809-1 
3851-7 

3770  6 
3813-4 
3855-9 

3774-9 
3817-6 
3860-2 

4  3 
4-3 
4-3 

166 
167 
168 

4  3864-4 
3906-8 
3949  0 

3868-7 
3911-0 
3953  2 

3872-9 
3915-2 
3957-4 

3877-2 
3919-5 
3961-6 

3881-4 
3923-7 
3965-8 

3885-6 
3927-9 
3970-0 

3889 
3932 
3974 

9 
1 
2 

3894-1 
3936  3 

3978-4 

3898-3 
3940  5 
3982-6 

3902-5 
3944-7 
3986-7 

4-2 
4-2 
4  2 

169 

170 
171 

4  3990-9 
4032-7 
407i  3 

3995-1 
4036  9 
4078-5 

3999  3 
40111 
4082-6 

4003-5 
4045-2 
4086-8 

4007-7 
4049-4 
4090-9 

4011-9 
4053-6 
4095-1 

4016 
4057 
4099 

0 
7 
2 

4020-2 
4061-9 
4103  3 

4024-4 
4066-0 
4107-5 

4028-6 
4070-2 
4111-6 

4-2 
4  2 
4  1 

172 
173 
174 

4  4115-7 
4157  0 
4198  0 

4119-9 
4161-1 
4202  1 

4124-0 
4165-2 
4206-2 

4128-1 
4169-3 
4210  3 

4132-3 

4173-4 
4214-4 

4136-4 

4177-5 
4218-5 

4140 

4181 
4222 

5 
6 
6 

4144-6 

4185-7 
4226-7 

4148-7 
4189-8 
4230-8 

4152-9 
4193-9 
4234-8 

4-1 
4  1 
4  1 

175 
176 

177 

4  4238  9 
4279  6 
4320  2 

4243  0 
4283-7 
4324-2 

4247-1 
4287-8 
4328-3 

4251-2 
4291-8 
4332 -3 

4255-3 
4295-9 
4336-4 

4259-3 
4300-0 
4340-4 

4263 
4304 
4344 

-4 
0 
-4 

4267-5 
4308-8 
4348  5 

4271-5 
4312-1 
4352-5 

4275-6 
4316  1 
4356-5 

4-1 
41 
4-0 

178 
179 
180 

4  4360-5 
4100  7 
4440-8 

4364-6 
4404-7 
4444-7 

4368-6 
4408  8 
4448-7 

4372-0 
4412-8 
4452-7 

4376-6 
4416  8 
4456-7 

4380-7 
4420-8 
4460-7 

4384 
4424 
4464 

-7 
-8 
7 

4388-7 
4428-8 
4468-7 

4392  7 
4432  8 
4472-6 

4396-7 
4436-8 
4476-6 

40 
4  0 
40 

181 
182 
183 

4  4480  6 
4520-3 
4559-8 

4484-6 
4524-2 
4563-7 

4488  5 
4528-2 
4567-7 

4492  5 
4532-2 
4571-6 

4496-5 
4536  1 
4575-6 

4500  5 
4540-1 
4579-5 

4501 
4544 
4583 

•4 
0 
4 

4. '08 -4 
4518  0 
4587-4 

4512-4 
4551-9 
4591-3 

4516-3 
4555  9 
4595-2 

4-0 
40 
3-9 

XX. — EXTERIOR    BALLISTICS. 


61 


Table  III . — Continued. 
Distance  and  Velocity  Table,  Cs  —  a^'  —  cr^„. 


V. 

0 

1 

2 

3 

4 

5 

6 

7 

8 

9 

Diffi 

f.s. 

184 
185  ! 
186 

feet. 

4  4599-2 
4638-4 
4677-4 

feet. 
4603-1 
4642-3 
4681-3 

feel 
4607 
4646 
4685 

0 

2 
2 

feet 
4610 
4650 
4689 

9 

feet. 
4614-9 
4654  0 
4693-0 

feel 

4618 
4657 
4696 

8 
9 
9 

feet. 

4622-7 
4661-8 
4700  8 

feel 

4626 
4665 
4704 

6 

7 
6 

feet. 

4630-5 
4669-6 
4708-5 

feet. 
4634-4 
4673  5 
4712-4 

+ 
3-9 
3-9 
3-9 

187 
188  ' 
189 

4  4716  3 
4755  0 
4793  7 

4720-2 
4758-9 
4797-5 

4724 
4762 
4801 

1 

8 
4 

4727 
4766 
4805 

4731-8 
4770  5 
4809-1 

4735 

4774 
4812 

7 
4 
9 

4739-6 
4778-2 
4816-8 

4743 
4782 
4820 

4 

1 
6 

4747-3 
4786-0 
4824-5 

4751-2 
4789-8 
4828-3 

3  9 
3  9 
3  8 

190 

191  i 

192  j 

4  4832-2 
4870-5 
4908-7 

4836  0 

4874-3 
4912  5 

4839 
4878 
4916 

8 
1 
3 

4843 

4882 
4920 

4847-5 
4885-8 
4923-9 

4861 
4889 
4927 

4 
6 

7 

4855-2 
4893  4 
4931-5 

4859 
4897 
4935 

0 
3 
3 

4862-8 
4901-1 
4939-1 

4866-7 
4904-9 
4942-9 

3  8 
3  8 
3  8 

193  i 

194 

195 

4  4946-7 
4984-5 
5022  2 

4950-5 
4988-3 
5025  9 

4954 
4992 
5029 

3 

1 
7 

4958 
4995 
5033 

4961-9 
4999  6 
6037-2 

4965 
5003 
5040 

7 
4 
9 

4969-4 
5007-1 
5044-7 

4973 
5010 

5048 

2 
9 
4 

4977-0 
5014  7 
5052-1 

4980-7 
5018-4 
5055-9 

3-8 
3-8 
3  7 

196 
197 

198  , 

4  5059-6 
5096-9 
5133-9 

5063-4 
5100  6 
6137-5 

5067 
5104 
6141 

1 
3 
2 

5070 
5108 
5144 

8 
0 
9 

5074-6 
5111-7 
5148  6 

5078 
5115 
5152 

3 

4 
3 

5082-0 
5119  1 
5150-0 

5085 
5122 
5159 

7 
8 
6 

6089-4 
5126-5 
5163-3 

5093  1 
5130  2 
6166  9 

3-7 
3-7 
3  7 

199 
200 
201 

4  5170-6 
5207-1 
5243-3 

5174-3 
5210-7 
6246-9 

5177 
5214 
5250 

9 
3 
5 

5181 
5218 
5254 

6 
0 

1 

5185-2 
5221-6 

5257-7 

5188 
5225 
5261 

9 
2 
3 

5192-5 
5228-8 
6264-9 

5196 
5232 
5268 

2 
5 
5 

5199-8 
5236-1 
5272-1 

5203-4 
5239-7 
5275  7 

3  6 

3  6 
3  6 

202 

203 
204 

4  5279  2 
631  i  9 
6360-3 

5282  8 
6318-5 
5353-8 

5286 
5322 
5357 

4 
0 
3 

5290 
5325 
5360 

0 
6 
9 

5293-0 
5329-1 
6364-4 

5297 
5332 
5367 

2 

7 
9 

5300-7 
5336  2 
6371-4 

5304 
5339 
5374 

3 

7 
9 

5307-8 
5343-3 
5378-4 

5311  4 
5346  8 
5391  9 

3  6 
3  5 
3-5 

205 
206 
207 

4  5385-4 
6420-2 
5454-7 

5388  9 
5423-7 
6458-1 

5392 
5427 
5461 

4 

1 
6 

5395 
5430 
5465 

9 
6 
0 

5399-4 
5434-1 
6468-4 

5402 

5437 
5471 

9 
5 
9 

5406-3 
5441  0 
5475-3 

5409 
5444 
5478 

8 
4 

7 

5413-3 
5447-8 
5482-1 

5416-7 
5451-3 
5485-6 

3  5 
3  5 
3  4 

208 

209  ! 

210  ' 

4  5488-9 
5522-8 
5556  4 

5492-3 
5526  2 
5559-8 

6495 
5529 
6563 

7 
6 
1 

5499 
5532 
6566 

1 
9 
4 

5502-5 
5536-3 
5569  8 

5505 
5539 
6573 

9 

7 
1 

5509  3 
5543  0 
6576  5 

5512 
5546 
5579 

7 
4 
8 

5516-1 
5549-7 
5583-1 

6519-4 
5553-1 
6586-4 

3  4 
3  4 
3-3 

211 
212 
213 

4  5589-7 
6622-8 
5655-5 

5593  0 
6626-1 
6658-8 

5596 
5029 
5662 

4 

3 
0 

5599 
5632 
5665 

7 
6 
3 

5603-0 
5635-9 
5668-6 

5606 
5639 
5671 

3 

2 
8 

5609-6 
5642-5 
6675  - 1 

5612 
5645 
5678 

9 

7 
3 

5616-2 
5649-0 
5681-5 

5619-5 
5652-3 
5684-8 

3  3 
3-3 
3-2 

214  ' 

215  ! 
216 

4  5688  0 
6/20-2 
6752-2 

5691  2 
5723-4 
5755-4 

5694 

5726 
5758 

5 
6 
6 

5697 
5729 
5761 

7 
9 
8 

5700-9 
5733-1 
6764  9 

5704 
5736 
5768 

2 
3 

1 

5707-4 
5739-5 
6771-3 

5710 

5742 

5774 

6 

6 
4 

5713-8 
5745-8 
5777-6 

5717-0 
6749-0 
6780  8 

3  2 
3  2 
3  2 

217  ' 

218 

219 

4  5783  9 
5815-4 
5846  6 

5787-1 
5818-5 
5849  7 

6790 
5821 
6852 

2 
6 
8 

5793 
5824 
5855 

4 
8 
9 

5796-6 
5827-9 
5859  0 

5799 
5831 
5862 

7 
0 
1 

5802-9 
6834  1 
5865-2 

5806 
5837 
5868 

0 
3 
3 

5809-1 
5840-4 
5871-4 

5812-2 
6843  5 
5874-4 

3  1 
3  1 
3  1 

220 
221 
222 

4  5877-5 
5908  3 
5938-7 

5880-6 
5911  3 
5941-8 

«883 
5914 
6944 

7 
4 
8 

5886 
5917 
5947 

8 
4 
8 

6889-9 
5920-5 
5950-9 

5893 
6923 
5963 

0 
6 
9 

5896-0 
5926-6 
5956-9 

5899 
5929 
5959 

1 
6 
9 

5902-1 
5932-7 
6963-0 

5905  2 
5935-7 
5966-0 

3  1 
3  0 
3  0 

223 
224  : 
225 

4  5969-0 
5999  0 
6028  7 

5972-0 
6002  0 
6031  7 

5975 
6004 
6034 

0 

9 
6 

6978 
6007 
6037 

0 
9 
6 

5981  0 
6010  9 
6040-5 

5984 
6013 
6043 

0 

9 
5 

5987-0 
6016  9 
6046  5 

5990 
6019 
6049 

0 

8 
4 

5993-0 
60-22  8 
6052  4 

5996-0 
6025-8  1 
6055  3  j 

6084  7  ' 

6113-8 

6142-8 

30 
3  0 
3  0 

226 

227  j 

228 

4  0058-3 
6087-6 
6116-7 

6061-2 
6090  5 
6119  6 

6064 
6093 
6122 

1 
4 
5 

0067-1 
C0'.)6  3 
6125  4 

0070-0 
6099-3 
6128  3 

6072 
6102 
6131 

9 
2 

-2 

6075-9 
6105  1 
6134  1 

6078 
6108 
6137 

8 
0 
0 

6081-7 
6110  9 
0139-9 

2  9 
2  9 
29 

2^-0  ^ 

4  6145 -7 
6174-6 

6148-6 
6177-5 

6151  5 
6180-4 

6154-4 
6183-3 

6157  3 
6186-2 

6160 
6189 

1 

4 

6163  1 
6191-9 

6166 
6194 

0 

8 

6168  8 
6197-7 

6171  7 
6200-6 

2-9 
2  9 



62 


XX. — EXTERIOR    BALLISTICS. 


Table  IV.* 
Inclination  and  Velocity  Table,  Cd  —  d^,  —  S^„. 


V. 

0 

1 

2 

3 

4 

5 

6 

7 

8 

9 

f.8. 

40 
41 
42 

d( 

4 
9 

?g8. 
0 

6757 
0056 

Cl( 

5 
9 

3g8. 
4838 
1240 
4207 

d 

5 
9 

9640 
5688 
8327 

d( 

1 

6 

10 

4407 
0101 
2410 

d( 

1 

6 

10 

3ff8. 
9137 
4482 
6467 

d 

2 

6 

11 

3^8. 
3830 
8828 
0496 

d 

2 

7 

11 

3S8. 
8488 
3141 
4494 

d 

3 

7 

11 

3110 

7421 
8462 

d 

8 
12 

3^8. 
7689 
1660 
2397 

degs. 

4-2240 

8-5874 

12-6306 

43 

13 
16 
20 

0187 
7450 
2125 

13 
17 
20 

4039 
1030 
5460 

13 
17 
20 

7862 
4585 
8772 

14 
17 
21 

1652 
8110 
2054 

14 
18 
21 

5419 
1614 
5320 

14 
18 
21 

9159 

5094 
8565 

15 

18 
22 

2872 
8549 
1788 

15 
19 
22 

6557 
1980 
4989 

16 
19 
22 

0211 
5383 
8169 

16-3843 
19.8766 
23  1327 

46 
47 

48 

23 
26 
29 

4463 
4691 
3006 

23 
26 
29 

7578 
7607 
5739 

24 
27 
29 

0671 
0503 
8455 

24 

27 
30 

3736 
3376 
1151 

24 

27 
30 

6788 
6234 
3833 

24 
27 
30 

9821 
9075 
6498 

25 
28 
30 

2C34 
1897 
9147 

25 
28 
31 

5927 
4702 
1779 

25 
28 
31 

8801 
7486 
4393 

26  1756 
29-0254 
31-6993 

49 
60 

ei 

31 
34 
36 

9576 

4557 
8073 

32 
34 
37 

2143 
6973 
0349 

32 
34 
37 

4695 
9375 
2613 

32 
35 
37 

7227 
1761 
4862 

32 
35 
37 

9747 
4134 
7099 

33 

35 
37 

2253 
6493 
9323 

33 

35 
38 

4743 
8837 
1534 

33 
36 
38 

7219 
1167 
3731 

33 

36 
38 

9679 
3480 
5914 

34  2125 
36-5783 
38-8086 

52 
53 

54 

39 
41 
43 

0246 
1175 
0967 

39 
41 
43 

2394 
3204 

2887 

39 
41 
43 

4529 
5221 
4795 

39 
41 
43 

6651 
7225 
6690 

39 
41 
43 

8762 
9221 
8578 

40 

42 
44 

0860 
1205 
0456 

40 

42 
44 

2947 
3179 
2324 

40 
42 
44 

5022 
5142 
4182 

40 
42 
44 

7083 
7095 
6031 

40-9135 
42-9037 

44-7870 

55 
56 
57 

44 
46 
48 

9698 
7437 
4270 

45 
46 
48 

1510 
9160 
5906 

45 

47 
48 

3325 
0874 
7534 

45 

47 
48 

5122 
2581 
9153 

45 
47 
49 

6910 
4277 
0764 

45 
47 
49 

8689 
5965 
2368 

46 

47 
49 

0457 
7644 
3963 

46 

47 
49 

2217 
9314 
5551 

46 
48 
49 

3964 
0973 
7130 

46-5705 
48-2625 
49-8701 

58 
59 
60 

50 
51 
53 

0265 
5492 
0003 

50 
51 
53 

1822 
6975 
1417 

50 
51 
53 

3370 

8451 
2825 

50 
51 
53 

4909 
9917 
4224 

50 
52 
53 

6442 

1378 
5618 

50 
52 
53 

7968 
2832 
7005 

50 
52 
53 

9487 
4280 
8386 

51 
52 
53 

0999 
5721 
9761 

51 
52 
54 

2505 
7155 
1130 

51-4002 

52-8583 
54-2492 

61 
62 
63 

54 
55 
56 

3847 
7054 
9663 

54 
55 

57 

5196 
8342 
0891 

54 
55 
57 

6539 
9623 
2114 

54 
56 

57 

7875 
0899 
3330 

54 
56 
57 

9205 
2169 
4542 

55 
56 

57 

0529 
3433 
5749 

55 
56 
57 

1846 
4690 
6950 

55 
56 

57 

3158 
5942 
8146 

55 
56 

57 

4462 
7188 
9338 

55-5761 
56-8428 
58-0523 

64 
65 

66 

58 
59 
60 

1703 
3209 
4207 

58 
59 
60 

2878 
4332 
5280 

58 
59 
60 

4046 
5449 
6348 

58 
59 
60 

5209 
6562 
7411 

58 
59 
60 

6367 
7669 
8470 

58 
59 
60 

7521 
8772 
9523 

58 
59 
61 

8669 
9869 
0572 

58 
60 
61 

9832 
0961 
1616 

59 
60 
61 

0949 
2047 
2654 

59-2081 
60  3130 
61-3688 

67 
68 
69 

61 
62 
63 

4719 
4779 
4414 

61 

62 
63 

5744 
5761 
5356 

61 
62 
63 

6766 
6739 
6294 

61 
62 
63 

7783 
7711 

7227 

61 
62 
63 

8796 
8680 
8157 

61 
62 
63 

9804 
9646 
9084 

62 
63 
64 

0808 
0607 
0006 

62 
63 

64 

1807 
1565 
0924 

62 
63 
64 

2802 
2519 
1838 

62  3793 
63-3468 
64  2749 

70 
71 

72 

64 
65 
66 

3656 
2522 
1015 

64 
65 
66 

4559 
3388 
1845 

64 
65 
66 

5459 
4250 
2671 

64 
65 
66 

6356 
5107 
3494 

64 
65 
66 

7249 
5962 
4313 

64 
65 
66 

8137 
6813 
5128 

64 
65 
66 

9022 
7660 
5940 

64 
65 
66 

9903 
8504 
6749 

65 
65 
66 

0779 
9345 
7553 

65-1652 
66-0182 
66-8355 

73 
74 
75 

66 
67 
68 

9153 
6955 
4436 

66 

67 
68 

9949 
7717 
5168 

67 
67 
68 

0740 
8476 
5896 

67 
67 
68 

1529 
9231 
6620 

67 
67 
68 

2314 
9983 
7342 

67 
68 
68 

3096 
0733 
8062 

67 
68 
68 

3875 
1479 
8778 

67 
68 
68 

4649 
2223 
9492 

67 
68 
69 

5422 
2964 
0204 

67-6190 
68-3702 
69  0912 

76 

77 
78 

69 
69 
70 

1617 
8497 
5082 

69 
69 
70 

2318 
9169 
5725 

69 
69 
70 

3017 
9838 
6365 

69 
70 
70 

3712 
0503 
7004 

69 
70 
70 

4404 
1166 
7639 

69 
70 
70 

5094 
1826 
8271 

69 
70 
70 

5780 
2483 
8901 

69 
70 
70 

6464 
3137 
9527 

69 
70 
71 

7145 
3787 
0149 

69-7823 
70-4436 
71-0770 

79 
80 
81 

71 
71 
72 

1388 
7432 
3225 

71 
71 

72 

2004 
8023 
3791 

71 
71 

72 

2617 
8611 
4354 

71 

71 

72 

3228 
9196 
4915 

71 
71 

72 

3837 
9779 
5473 

71 

72 
72 

4442 
0359 
6030 

71 

72 
72 

5045 
0937 
6584 

71 

72 
72 

5646 
1513 
7135 

71 

72 
72 

6244 
2086 
7685 

71-6839 
72  2656 
72-8232 

82 
83 

84 

72 
73 
73 

8776 
4079 
9143 

72 
73 
73 

9317 
4596 
9636 

72 
73 
74 

9856 
5111 
0127 

73 

73 
74 

0393 

5622 
0615 

73 
73 

74 

0927 
6132 
1101 

73 
73 
74 

1458 
6639 
1585 

73 
73 

74 

1988 
7145 
2067 

73 
73 

74 

2514 
7648 
2546 

73 

73 

74 

3038 
8149 
3023 

73-3560 
73-8647 
74-3498 

85 
86 
87 

74 
74 
75 

3971 
8573 
2966 

74 
74 
75 

4441 
9022 
3395 

74 
74 
75 

4910 
9468 
3821 

74 
74 
75 

5376 
9912 
4246 

74 
75 
75 

5839 
0355 
4668 

74 
75 
75 

6301 
0795 
5089 

74 
75 
75 

6760 
1233 
5507 

74 
75 
75 

7217 
1669 
5924 

74 
75 
75 

7670 
2104 
6339 

74-8123 
75-2536 
75-6752 

By  W.  D.  Kiven,  Esq.,  M.  A.,  F.  S.  S. 


XX. EXTERIOR    BALLISTICS. 


Table   lY  .—Continued. 
Inclination  and  Velocity  Table,  Cd  =  8^  —  S^„ 


V. 

0 

1 

!3 

3 

4 

5 

6 

7 

8 

9 

f.8. 

88 

89  1 
90 

degs. 

75  7163 

76  1171 
76-5005 

degs. 
75-7572 
76-1562 
76-5379 

degs. 
75-7980 
76-1952 
76-5751 

degs. 

75  8385 
76-2339 

76  6121 

degs. 

75-8788 
76-2725 
76-6490 

degs. 

75-9190 

i  76-3109 

76-6857 

degs. 
75  9590 
76-3492 
76-7223 

degs. 
75-9988 
76-3873 
76-7588 

d 

76 
76 
76 

4252 
7951 

degs. 
76-0778 
76-4629 
76  8312 

91 
92 
93 

76-8671 
77-2179 
77-5540 

76-9029 
77-2522 
77-5868 

76-9385 
77-2863 
77-6195 

76-9739 
77-3203 
77-6520 

77-0092 
77-3541 
77-6844 

77-0444 

77-3878 
77-7167 

77  0794 
77  4213 

77-7488 

77-1142 

77-4547 
77-7807 

77 
77 
77 

1489 
4879 
81-25 

77-1835 
77-5210 
77  8442 

94 

95 
96 

77-8757 
78  1841 
78-4798 

77  9071 
78-2142 

78  5087 

77-9384 
78-2442 
78-5375 

77-9695 
78-2741 
78-5622 

78-0005 
78  3039 
78-5947 

78-0314 
78-3335 
78-6231 

78  0622 
78-3630 
78-6514 

78-0929 
78-3924 
78-6796 

78 
78 
78 

1234 
4216 
7076 

78  1538 
78  4508 
78  7356 

97 
98 
99 

78-7634 
79-0354 
79-2968 

78-7911 
79  0621 
79-3224 

78-8188 
79-0886 
79-3478 

78  8463 

79  1150 
79-3731 

78-8736 
79  1413 
79-3983 

78-9009 
79  1675 
79-4234 

78-9280 
79  1936 
79-4484 

78-9551 
79-2195 
79-4734 

78 
79 
79 

9819 
2454 
4982 

79-0087 
79-2712 
79  5230 

100 
101  1 
102 

79-5476 
79-7889 
80-0203 

79-5722 
79-8124 
80  0430 

79-5966 
79-8359 
80-0655 

79-6210 
79-8593 
80-0879 

79-6453 
79-8826 
80  1102 

79  6695 
79-9058 

80  1324 

79-6935 
79  9289 
80-1544 

79-7175 
79-9519 
80-1763 

79 
79 
80 

7414 
9748 
1981 

79  7652 
79-9976 
80-2197 

103 
104 

105 

80-2412 
80-4466 
80-6321 

80-2625 
80-4661 
80-6495 

80-2837 
80-4854 
80-6667 

80-3408 
80-5045 
80-6835 

80-3256 
80  5234 
80  7003 

80-3462 
80  5420 
80  7169 

80  3667 
80  5605 
80  7333 

80-3869 
80-5787 
80-7495 

80 
80 
80 

4071 

5967 
7654 

80-4270 
80  6145 
80  7813 

106 

107  ' 

108  1 

80  7970 
80-9463 
81-0841 

80-8126 
80-9606 
81-0973 

80-8280 
80-9747 
81  1105 

80-8432 
80-9886 
81  1236 

80-8583 
81  0026 
81  1366 

80-8733 

I  81  0164 

81  1495 

80-8882 
81-0301 
81  1624 

80  9029 

81  0437 
81  1751 

80 
81 
81 

9175 
0573 
1877 

80-?319 
81  0707 
81  2003 

109 
110 
lllj 

81-2129 
81-3342 
81-4495 

81-2253 
81-3460 
81-4607 

81-2377 
81-3578 
81-4719 

81  2501 
81  3695 
81  4829 

81-2623 
81-3811 
81  4939 

81-2745 
81-3927 
81  5049 

81-2866 
81-4042 
81-5159 

81-2986 
81-4156 
81-5268 

81 
81 
81 

3105 
4269 
5377 

81-3224 
81  4382 
81  5486 

112 
113 
114  ! 

81-5593 
81-6647 
81  7662 

81-5700 
81-6750 
81-7761 

81-5807 
81-6853 
81-7861 

81-5913 
81-6955 
81-7960 

81-6019 
81-7057 
81-8058 

81-6124 
81  7159 
81-8156 

81-6230 
81-7260 
81-8254 

81-6334 
81-7361 
81-8351 

81 
81 
81 

6439 

7462 
8448 

81-6543 
81-7662 
81 •8545 

115 
116 
117 

81-8641 
81-9588 
82-0503 

81-8737 
81-9681 
82-0592 

81-8833 
81-9774 
82-0682 

81-8929 
81-9866 
82  0771 

81-9024 
81-9958 
82-0860 

81-9119 
82-0049 
82  0948 

81-9213 
82  0141 
82  1036 

81-9307 
82-0232 
82  1124 

81 
82 
82 

9401 
0322 
1212 

81-9496 
82  0413 
82-1299 

118 
119 
120 

82  1386 
82-2241 
82-3066 

82-1473 
82-2325 
82-3147 

82  1559 
82-2408 
82-3228 

82  1645 
82-2492 
82  3309 

82  1731 
82-2575 
82-3389 

82-1817 
82-2657 
82-3469 

82-1902 
82-2Y40 
82-3549 

82-1988 
82-2822 
82-3629 

82 
82 
82 

2073 
2903 
3708 

82-2157 
82-2985 
82-3787 

121 
122 
123 

82-3865 
82-4639 
82  5386 

82-3944 
82-4715 
82-5459 

82-4022 
82-4790 
82  5533 

82-4100 
82-4865 
82-5606 

82-4178 
82-4940 
82-5679 

82-4255 
82  5015 
82-5751 

82-4333 
82-5090 
82-5824 

82-4410 
82-5164 
82-5896 

82 
82 
82 

4486 
5238 
5968 

82-4563 
82-5312 
82  6040 

124 
125 
126 

82-6112 
82-6814 
82-7494 

82-6183 
82-6883 
82-7561 

82-6254 
82-6951 
82-7627 

82  6324 
82-7019 
82  7694 

82-6395 
82-7088 
82  7760 

82-6465 
82-7156 
82-7826 

82-6535 

82-7224 
82-7892 

82-6605 
82-7291 
82-7957 

82 

82 
82 

6675 
7359 
8023 

82-6744 
82-7427 
82-8088 

127 
128 
129 

82-8153 
82-8794 
82-9415 

82-8218 
82-8857 
82-9477 

82-8283 
82-8920 
82-9538 

82-8348 
82-8983 
82-9599 

82-8412 
82-9045 
82-9660 

82-8477 
82-9107 
82-9720 

82-8541 
82-9169 
82-9780 

82-8604 
82-9231 
82-9840 

82 
82 
82 

8668 
9292 
9900 

82-8731 
82-9354 
82-9900 

130 
131 
132 

83-0019 
83  0606 
83  1176 

83-0079 
83-0664 
83  1232 

83-0138 
83-0721 
83-1288 

83  0197 
83-0779 
83-1344 

83-0256 
83-0836 
83-1400 

83  0315 
83-0893 
83  1455 

83-0373 
83  0950 
83  1511 

83-0432 
83-1007 
83  1566 

83 
83 
83 

0490 
10^3 
1621 

83  0548 
83-1119 
83-1676 

133 
184 
136 

83-1730 
83-2271 
83-2797 

83-1785 
83-2324 
83-2849 

83  1840 
83-2377 
83-2900 

83-1894 
83-2430 
83-2951 

83  1949 
83-2483 
83-3003 

83-2003 
83-2536 
83-3054 

83-2057 
83-2588 
83-3105 

83  2110 
83-2641 
83-3156 

83 
83 
83 

2164 
2693 
3207 

83  2217 
83  2745 
83-3257 

64 


XX. — EXTERIOR    BALLISTICS. 


Table   lY .—Continued. 
Inclination  and  Velocity  Table,  Cd  =  d^, 


.. 

0 

1 

2 

3 

4 

5 

6 

7 

8 

" 

f.s. 

136 
137 
138 

degs. 
83-3308 
83-3808 
83-4295 

d( 

83 
83 
83 

5gS. 
3359 
3857 
4343 

degs. 
83-3409 
83-3906 
83-4391 

degs. 

83-3459 
83-3955 
83-4438 

d( 

83 
83 
83 

3509 
4004 
4486 

d( 

83 
83 
83 

3560 
4053 
4533 

d< 

83 
83 
83 

3g8. 
3609 
4101 

4581 

d( 

83 
83 

83 

5g8. 
3659 
4150 
4628 

d( 

83 

83 
83 

3g8. 
3709 
4198 
4676 

degs. 
83-3759 
83-4247 
83-4723 

139 
140  ' 
141 

83 
83 
83 

4770 
5233 
5687 

83 
83 
83 

4817 
5279 
5732 

83-4863 
83-5325 
83-5777 

83-4910 
83-5371 
83-5821 

83 
83 
83 

4956 
5417 
5866 

83 
83 
83 

5003 

5402 
5910 

83 
83 
83 

5049 
5507 
5954 

83 
83 
83 

5095 
5553 
5999 

83 
83 
83 

5141 
5598 
6043 

83-5187 
83-5642 
83-6087 

142 
143 
144 

83 
83 
83 

6130 
6565 
6988 

83 
83 
83 

6174 
6607 
7030 

83-6218 
83  -  0650 
83-7072 

83-6261 
83-6693 
83-7114 

83 
83 
83 

6305 
6735 
7156 

83 
83 
83 

6348 
6778 
7197 

83 
83 
83 

6392 
6820 
7239 

83 
83 
83 

6435 

6862 
7280 

83 
83 
83 

6478 
6904 
7321 

83-6522 
83-6946 
83-7362 

145  \ 

146  i 
147 

83 
83 
83 

7403 
7810 
8209 

83 
83 
83 

7444 
7850 
8249 

83-7485 
8.3-7891 
83-8-288 

83-7526 
83-7930 
83  8327 

83 
83 

7567 
7970 
8366 

83 
83 
83 

7608 
8010 
8406 

83 

83 
83 

7649 
8050 
8445 

83 
83 
83 

7689 
8090 
8484 

83 
83 
83 

7730 
8130 
8522 

83-7770 
83 '8170 
83-8561 

148 
149 
150 

83 
83 
83 

8600 
8983 
9359 

83 
83 
83 

8639 
9021 
9396 

83-8677 
83-9059 
83-9433 

83-8715 
83  9096 
83-9470 

83 
83 

83 

8754 
9134 
9507 

83 
83 
83 

8792 
9172 
9544 

83 
83 
83 

8830 
9209 
9581 

83 
83 
83 

8869 
9247 
9617 

83 
83 
83 

8907 
9285 
9654 

83-8945 
83-9322 
83-9691 

151  ' 

152 

153 

83 
84 
84 

9727 
0090 
0446 

83 
84 
84 

9764 
0126 
0481 

83-9800 
84-0161 
84-0516 

83-9837 
84-0197 
84-0551 

83 
84 
84 

9873 
0233 
0587 

83 
84 
84 

9909 
0269 
0622 

83 
84 
84 

9946 
0304 

0657 

83 
84 
84 

9982 
0340 
0692 

84 
84 
84 

0018 
0375 
0727 

84-0054 
84-0410 
84-0762 

15. 
155 

156 

84 
84 
84 

0796 
1140 
1479 

84 
84 
84 

0831 
1174 
1513 

84-0866 
84  1208 
84-1546 

84-0900 
84-1242 
84-1579 

84 
84 
84 

0935 
1276 
1613 

84 
84 

84 

0969 
1310 
1646 

84 
84 
84 

1004 
1344 
1679 

84 
84 
84 

1038 
1378 
1713 

84 
84 
84 

1072 
1412 
1746 

84-1106 
84  1445 
84-1779 

157 
158 
159 

84 
84 
84 

1812 
2139 
2461 

84 
84 
84 

1845 
2172 
2493 

84-1878 
84-2204 
84-2525 

84-1911 
84-2237 
84-2557 

84 
84 
84 

1943 
2269 
2588 

84 
84 
84 

1976 
2301 
2620 

84 
84 
84 

2009 
2333 
2652 

84 
84 
84 

2041 
2366 
2683 

84 
84 
84 

2074 
2398 
2715 

84-2107 
84-2430 
84-2746 

160  ' 

161 

162 

84 
84 
84 

2778 
3088 
3394 

84 
84 
84 

2809 
3119 
3424 

84-2840 
84-3150 
84-3454 

84-2871 
84-3180 
84-3484 

84 
84 
84 

2902 
3210 
3514 

84 

84 

,84 

2933 
3242 
3544 

84 

84 
84 

2965 
3272 
3574 

84 
84 

84 

2996 
3302 
3604 

84 
81 
84 

3027 
3333 
3634 

84-3058 
84-3363 
84-3664 

163 
164 
165 

84 
84 
84 

3694 
3990 
4281 

84 
84 
84 

3724 
4019 
4310 

84-3753 
84-4018 
84-4339 

84-3783 
84-4078 
84-4367 

84 
84 
84 

3813 
4107 
4396 

84 
81 
84 

3843 

41S6 
4425 

84 
84 
84 

3872 
4105 
4453 

84 
84 
84 

3902 
4194 

4482 

84 
84 
84 

3931 
4223 
4510 

84-3960 
84-4252 
84-4539 

166 
137 
168 

84 
84 
84 

4567 
4849 
5127 

84 
84 
84 

4595 
4877 
5154 

84-4624 
84-4905 
84-5181 

84-4652 
84-4933 
84-5209 

84 
84 
84 

4680 
4961 
5236 

84 
84 
84 

4709 
4988 
5263 

84 
84 
84 

4737 
5016 
5291 

84 
84 
84 

4765 
5044 
5318 

84 
84 
84 

4793 
5070 
5345 

84-4821 
84-5099 
84-5372 

169 
170 
171 

84 
84 
84 

5399 
5668 
5933 

84 
84 
84 

5426 
5695 
5959 

84-5453 
84-5721 
84-5985 

84-5480 
84-5748 
84-6012 

84 
84 
84 

5508 

5775 
6038 

84 
84 
84 

5534 
6801 
6064 

84 
84 
84 

5561 
5828 
6090 

84 
84 
84 

5588 
5854 
6116 

84 

84 
84 

5615 
5880 
6142 

84-5641 
84-5907 
84  0168 

172 
173 
174 

84 
84 

84 

6193 
6449 
6701 

84 
84 
84 

6219 
6475 
6726 

84-6245 
84-6500 
84-6750 

84-6271 
84-6525 
84-6776 

84 
84 
84 

6297 
6550 
6800 

84 
84 
84 

6322 
6575 
6825 

84 
84 
84 

6348 
6001 
6850 

84 

84 
84 

6373 
6626 
6875 

84 
84 
84 

6399 
6651 
6899 

84-6424 
84-6676 
84-6924 

175 
176 

177 

84 
84 
84 

6948 
7192 
7432 

84 
84 
84 

6973 
7216 
7455 

84-6997 
84-7240 
84-7479 

84-7022 
84-7264 
84-7503 

84 
84 
84 

7046 
7288 
7526 

84 
84 
84 

7071 
7312 
7550 

84 
84 
84 

7095 
7336 
7574 

84 
84 
84 

7119 
7360 
7597 

84 
84 
84 

7144 
7384 
7621 

84-7168 
84-7408 
84-7645 

178 
179 
180 

81 
84 
84 

7608 
7P02 
8131 

84 
81 
84 

7692 
•7925 
8154 

81 -771 5 
84-7918 
84-8177 

84-7739 
81-7972 
8i-8199 

84 

81 
84 

7762. 
7904 
8222 

•84 
81 
81 

7785 

roi7 

8214 

84 
84 
84 

7809 

80  :o 

82u7 

84 
84 
84 

7832 
803 
8289 

84 
84 
84 

7855 
80SG 
8312 

84-7878 
81-8109 
84-8334 

181 

182 
183 

84 
84 
84 

83R7 
8579 
8798 

81 

84 
84 

8379 
8601 
8819 

84-8-101 
84-8623 
84-8841 

81 ■ 8424 
84-8645 
84-8863 

84 
84 

84 

8446 
8667 
8884 

84 
i  ^* 

8168 
8689 
8906 

84 
84 

84 

81 PO 

8711 
8927 

84 
84 
84 

8513 

8732 
8949 

84 
84 
84 

8535 
8754 
8970 

84-8557 
84-8776 
84-8992 

XX. — EXTERIOR    BALLIStlCS. 


Table  IV.— Continued. 
Inclination  and  Velocity  Table,  Cd  =  S^,  —  S^„. 


V. 

0 

1 

2 

3 

4 

5 

6 

7 

8 

0 

f.s. 

184 
185 
186 

d 

84 
84 
84 

9013 
9226 
9435 

d 

84 
84 
84 

egs. 
9035 
9247 
9456 

d 

84 
84 
84 

9056 
9268 

9476 

d 
84 
84 
84 

egs. 

9077 
•9289 

9497 

d 

84 
84 
84 

egs. 
•9099 
•9310 
9518 

d 

84 
34 
84 

9120 
9331 
•9538 

d 

84 
84 
84 

egs. 
9141 
9351 

•9559 

degs. 
84-9162 
84  9372 
84-9580 

d 

84 
84 
84 

egs. 
■9184 
■9393 
-9600 

degs. 

84-9205 
84  9414 
84-9621 

1?7 
188 
189 

84 
84 
85 

9C41 
•9845 
0045 

84 
84 
86 

9C62 
9865 
0065 

84 
84 
85 

9682 
9885 
0085 

84 
84 
85 

9702 
9905 
0105 

84 
84 
85 

9723 
9925 
0125 

84 
84 
85 

•9743 
•9946 
•0145 

84 
84 
85 

9763 
•9966 
0165 

84 • 9784 
84-9986 
85  0185 

84 
85 
85 

9804 
0006 
0204 

84-9820 
86-0026 
85-0224 

190 
191 
192 

85 

85 
85 

0244 
0438 
0630 

85 
85 
85 

0263 
0458 
0650 

85 
85 
85 

0283 
0477 
0669 

85 
85 
85 

0303 
0496 
0687 

85 
85 
85 

0322 
0515 
0706 

85 
85 
85 

0342 
0535 
0725 

85 
85 
85 

•0361 
0554 
0744 

85  0380 

86  0573 
85  0763 

85 
85 
85 

0400 
0592 
0782 

8.'5  0419 
85-0611 
85-0801 

193 
194 
195 

85 
85 
85 

0820 
1006 
1190 

85 
85 

85 

0838 
1025 
1208 

85 
85 
85 

0857 
1043 
1227 

86 
86 
85 

0876 
10C2 
1245 

85 
85 
85 

0895 
1080 
1263 

85 
85 
85 

0913 
1099 
1281 

85 
85 
85 

•0932 
1117 
1299 

85  0951 
85  1136 
85  1317 

85 
85 
85 

0969 
1154 
1335 

85-0988 
86  1172 
85 -136a 

196 
197 
198 

85 
85 
85 

1371 
1549 
1724 

85 
86 
85 

1389 
1567 
1741 

85 
85 

85 

1407 
1584 
1759 

85 
85 
85 

1425 
1602 
1776 

85 
85 
85 

1443 
1619 
1793 

85 
85 
85 

1460 
1637 
1810 

85 
85 
85 

1478 
1654 

1827 

85  1496 
85-1672 

85  1844 

85 
85 
85 

1514 
1689 
1862 

86-1531 
85  1707 
86-1879 

199 
200 
201 

85 
85 
85 

1896 
2065 
2231 

85 
85 
85 

1913 
2081 
2247 

85 
85 
85 

1930  ' 

2098 

2264 

86 
85 
85 

1947 
2115 
2280 

85 
85 
85 

1964 
2131 
2290 

84 
85 
85 

1981 
2148 
2313 

85 
85 
85 

1998 
2165 
2329 

85  2014 
85-2181 
85-2346 

85 
85 
85 

2031 
2198 
2362 

86-2043 
85-2214 
85-2378 

202 
203 
204 

85 
85 
85 

2394 

2556* 

2714 

85 
85 
85 

2411 

2572 
2729 

85 

85 
85 

2427 
2588 
2745 

85 
85 
86 

2443 
2604 
2760 

86 
85 
85 

2459 

2620 
2776 

85 

85 
85 

2476 
2635 
2791 

85 
85 
86 

2492 
2651 
2807 

85  2507 
85-2667 
85-2822 

85 

85 
86 

2524 
2682 
2838 

85-2540 
85-2698 
85-2863 

205 
206 
207 

85 
85 
85 

2868 
3020 
3170 

85 
86 
85 

2884 
3035 
3184 

86 
85 
85 

2899 
3061 
3199 

86 
85 
85 

2915 
3066 
3214 

85 
85 
85 

293C 
3081 
3229 

86 
85 

2945 
3095 
3244 

85 
85 
86 

2960 
3110 
3258 

85  2975 
85-3125 
85-3273 

85 

85 
85 

2990 
3140 

3287 

85-3005 
85  3165 
85-330a 

208 
209 
210 

85 
85 
85 

3316 
3460 
3601 

85 
85 
85 

3331 
3474 
3615 

85 
85 
85 

3345 
3488 
3629 

85 
85 
86 

3360 
3503 
3643 

85 
85 

85 

3373 
3517 
3657 

85 
85 
85 

3388 
3531 
3671 

86 
85 

85 

3403 
3546 
3685 

86  3417 
85-3559 
85-3698 

85 
85 
85 

3431 
3573 
3712 

85-3446 
85-3581 
85  3726 

211 
212 
213 

85 
85 
85 

3740 
3876 
4010 

85 

85 
88 

3754 
3890 
4023 

85 
85 
85 

3767 
3903 
4036 

85 
85 
85 

3781 
3917 
•4049 

85 

85 
85 

3795 
3930 
4063 

85 

85 
85 

3808 
3943 
4076 

85 
85 
85 

3822 
3957 
4089 

85  3836 
85  3970 
85-4102 

85 

85 
86 

3849 
3983 
4115 

85-3863 
85-3996 
85  4128 

21^ 
215 
216 

85 
85 
85 

4141 

4271 
4398 

85 
85 
85 

4154 
4284 
4411 

85 
86 
85 

4167 
4297 
4423 

85 
86 
85 

4180 
4309 
4436 

85 
85 
85 

4193 
4322 
4448 

85 
85 
85 

4206 
4335 
4461 

85 
85 
86 

4219 
4348 
4473 

85-4232 
85-4360 
85-4485 

86 
85 
85 

4245 
4373 

4498 

85-4258 
85-4385 
86-4510 

217 
218 
219 

85 
85 
85 

4523 
4645 
4766 

85 
85 

85 

4535 

4658 
4778 

85 
85 
85 

4547 
4670 
4790 

85 
85 
85 

4560 
4682 
4802 

85 
85 
86 

4572 
4694 
4814 

85 
85 
85 

4584 
4706 
4825 

85 
85 
85 

4597 
4718 
4837 

85-4609 
85-4730 
85-4849 

85 
85 
86 

4621 
4742 
4861 

86-4633 
86-4754 
86-4873 

220 
221 
222 

85 
85 
85 

4885 
5001 
5116 

85 
85 
85 

4896 
5013 
5128 

86 
85 
85 

4908 
5024 
5139 

85 
86 
86 

4920 
6036 
6150 

85 
85 
85 

4932 
5047 
5162 

86 
85 
85 

4943 
5059 
5173 

85 
85 
85 

4965 
6070 
6184 

85-4967 
85-5082 
85  5195 

86 
85 
86 

4978 
5093 
5207 

85-4990 
85-6105 
85-5218 

223 
224 
225 

85 
85 
85 

5229 
5340 
5449 

85 
85 
85 

5240 
5351 
5460 

85 
85 
85 

5251 
5362 
5470 

85 
85 
85 

5262 
5373 
6481 

85 
85 
85 

5273 
5384 
5492 

85 
85 
86 

5285 
5394 
5502 

85 
85 
85 

5296 
5405 
5513 

85-5307 
85-5416 
86-5624 

86 
85 
85 

5318 
5427 
5534 

85-5329 
86-5438 
86-6545 

226 
227 
228 

85 
85 
85 

5556 
5661 
5765 

85 
85 
85 

5566 
5672 
6775 

85 
85 
85 

5577 
5682 
5785 

85 
85 
85 

5688 
6693 
5796 

86 
85 
85 

6598 
5703 
5806 

86 
85 
85 

5609 
5713 
5816 

85 
86 
86 

5619 
5724 
5826 

85-5630 
85-5734 
85-5836 

85 
85 
85 

5640 

5744 
5846 

85-5651 
85-5755 
85-5856 

229 
230 

85 
85 

5866 
5966 

85 
85 

5876 
5976 

85 
85 

5886 
5986 

85 
85 

5896 
5996 

85 
85 

5906 
6006 

85 
85 

5916 
6015 

85 
85 

6926 
6025 

85  5936 
85-6035 

85 
85- 

5946 
6045 

85-5956 
85-6055 

XXI. — VARIETIES   OF    CANNON. 


CHAPTER  XXI. 

VARIETIES  OF  CANNON. 

CLASSIFICATION. 

The  numerous  ways  in  which  cannon  may  be  classified 
have  been  simpHfied  by  the  almost  universal  adoption  of 
those  which  are  breech-loading  rifies^  built  up  of  steel. 

For  convenience  of  treatment  we  may  consider  them  ac- 
cording to  t\\Q\v  proportions,  construction  and  service, 

1.  Proportions. 

The  facility  with  which  breech-loading  cannon  of  all 
lengths  may  be  loaded  has  practically  abolished  the  distinc- 
tion between  mortars  and  howitzers,  although  both  terms  are 
still  used  for  pieces  which  do  not  differ  materially  in  their 
proportions. 

It  has  become  customary  to  distinguish  guns  (Chapter  I) 
from  howitzers  by  calling  the  first  named  rifles,  although  all 
new  howitzers  are  also  rifled. 

2.  Construction. 

As  to  construction,  cannon  are  divided  into  muzzle-loaders 
and  breech-loaders;  some  of  the  former  class  being  still  re- 
tained in  service  pending  the  preparation  of  those  of  the  better 
type  and  also  for  subordinate  purposes. 

Breech-loaders  may  be  divided  into  those  having  but  one 
barrel,  or  single  fire  pieces,  which  are  loaded  by  hand,  and 
into  machine  guns,  in  which  the  loading  is  automatically  per- 
formed by  machinery.  The  former  may  be  either  the  com- 
paratively slow  fire  cannon,  in  which  the  cartridge  and 
projectile  are  loaded  separately,  or  the  rapid  fire  in  which 


XXI. VARIETIES    OF    CANNON. 


the  ammunition  makes  but  one  package,  as  in  small  arms, 
and  the  recoil  of  which  does  not  derange  the  aim. 

Machine  guns  generally  consist  of  a  number  of  barrels  so 
disposed,  that  while  one  is  firing,  the  remainder  may  be 
loaded  and  prepared  for  loading.  Like  the  rapid  fire  cannon 
these  require  metallic  ammunition,  and  unlike  them  their  size 
is  imited  by  the  weight  of  the  required  number  of  cartridges 
which  can  be  conveniently  kept  in  motion  by  the  machinery  ; 
the  latter  is  generally  operated  by  hand. 

3.  Service. 

According  to  their  employment,  cannon  are  divided  into 
those  for  the  mountain,  field,  siege  and  sea  coast  services. 

The  principal  distinction  here  refers  to  the  difficulties  of 
transportation,  for  the  rule  is  general  that  the  most  power- 
ful cannon  that  can  be  efficiently  transported  should  always 
be  employed. 

For  field  artillery  especially,  the  principle  of  independence 
of  function  requires  a  very  exact  adaptation  of  the  weight  of 
the  arm  to  the  service  required  of  it.  Thus,  we  have,  1st, 
Horse  Artillery,  which,  the  cannoneers  being  mounted  on 
horses,  may  accompany  the  Cavalry ;  2nd,  Light  Field  Ar- 
tillery, which  manoeuvres  with  Infantry  ;  and  3rd,  Heaiy  Field 
Artillery,  which  forms  batteries  of  position  at  important  tacti- 
cal points,  and  is  intended  to  engage  at  long  ranges. 

This  affords  the  following  table : 

CLASSIFICATION    OF    ARTILLERY    ACCORDING    TO 

1     P.-r,^^rt;r.nc       S  Guiis,  for  direct  fire. 

1.  rioporuons       ^  Howitzers,  or  Mortars  for  curved  fire. 

r  Muz  de  loading  ^Smoothbore. 

I  (obselete,  retained)      \  Rifled. 

2.  Construction     \  '  i  c-   „,     <-_  (  slow. 


'  *  (     ■  (  slow, 

j  Breech  loading  rifles     )  ^'"^le  fire  |  ^.^p- j^ 
(  Machine  guns, 


XXI. — VARIETIES   OF    CANNON. 


3.  Service. 


Mountain. 

i  Horse  Artillery,  very  light. 
Field       <  Light  Field  Artillery,  medium. 

f  Heavy  Field  Artillery. 
Siege. 
Sea  Coast. 


SYSTEM    OF    ARTILLERY. 


This  term  refers  to  the  character  and  arrangement  of  the 
materiel*  as  adopted  by  a  nation  at  any  particular  epoch. 

The  principal  requisites  of  a  system  of  artillery  are  sim- 
plicity^ mobility  and  power.  To  these  the  enormous  arma- 
ments of  the  present  day  may  add  economy. 

The  improvements  of  the  last  four  hundred  years  have  had 
these  qualities  in  view,  the  compromises  between  simplicity 
and  mechanical  efficiency,  noted  Chapter  XVI,  causing 
sometimes  one,  and  sometimes  another  of  these  qualities  to 
pieponderate. 

As  in  other  nations  the  system  of  artillery  in  the  United 
States  service  is  still  in  an  experimental  state. 

For  lack  of  funds,  withheld  largely  because  of  uncertainty 
regarding  the  direction  of  improvement,  many  obsolete 
weapons  have  been  retained  by  us  either  unchanged,  or 
converted  so  as  to  increase  their  power  at  a  moderate  expense. 

The  following  description  is  therefore  partly  historical,  and 
contains  incidental  reference  to  methods  adopted  in  other 
countries  whose  political  situation  has  made  their  immediate 
armament  urgent.  It  is  confined  to  slow  fire  guns,  since 
other  types  of  breech-loaders  depend  for  their  efficiency 
almost  wholly  upon  the  control  of  their  recoil  and  upon  the 
use  of  metaUic  ammunition;  subjects  not  yet  discussed.  See 
Chapter  XXIX. 

*  See  Webster, 


XXr. — VARIETIES    OF   CANNON. 


CONSTRUCTION. 

I.    MUZZLE    LOADING    CANNON. 

United  States. 

The  field  guns  used  during  the  Civil  War  were  of  two 
kinds. 

1.    The  3  ijich  wrought  iron  (10  pdr^  rifle. 

This  was  made  by  wrapping  boiler  plate  around  a  wrought 
iron  bar  to  form  a  rough  cyUnder,  which  was  welded 
together  under  the  rolls  and  finished  in  the  usual  manner. 

It  made  a  very  strong,  light  gun  well  adapted  to  the 
Horse  Artillery. 

2.   The  12  pdr.  Napoleon  Gun^  S7nooth  bore. 

This  was  of  bronze,  cast  solid.  Its  value  depended  upon 
the  topography  of  the  seat  of  war. 

The  broken  surface  of  the  Appalachian  system  and  the 
heavy  woods  with  which  much  of  the  country  was  covered 
restricted  the  fighting  to  ranges  which,  compared  to  those 
obtainable  on  the  broad  plains  of  Europe,  are  very  moderate. 
For  such  ranges  its  heavy  shell  and  well  filled  shrapnel  were 
more  efiective  than  those  of  the  rifle,  and  the  initial  velocity 
was  so  great  that  for  ranges  of  about  1000  yards  the  trajectory 
of  the  smooth  bore  was  flatter  than  that  of  the  rifle. 

The  siege  gims,  in  which  mobility  was  less  important,  were 
of  cast  iron.  Owing  to  the  length  of  the  bore  and  its  rela- 
tively small  diameter  these  guns  were  cast  solid.  The  pro- 
jectile weighed  about  30  pounds. 

One  of  these  pieces,  the  Parrott,  was  strengthened  by  a 
wrought  iron  cylinder  shrunk  over  the  breech  and  reinforce. 

In  order  to  prepare  so  massive  a  forging  a  hot  iron  bar  was 
coiled  helically  around  a  mandrel,  brought  to  a  welding  heat 
and   forged   by  axial  blows   of  the   hammer.     To  prevent 


XXr. — VARIETIES   OF   CANNON. 


distortion  during  welding,  the  coil  was  held  in  a  hollow  cyl- 
inder. Several  coils  would  be  similarly  welded  end  to  end. 
The  direction  of  the  fibers  gave  great  tangential  tenacity,  but 
for  reasons  given  in  Chapters  XV,  page  60,  and  XIX,  page 
12,  the  construction  was  faulty. 

Sea  coast  guns  were  generally  of  cast  iron,  cast  hollow  on 
the  Rodman  principle.  To  some  the  Parrott  construction 
was  applied. 

Since  1875  many  Rodman  guns  have  been  converted  on 
the  Palliser  (English)  plan  by  reaming  out  the  bores  to  receive 
a  thick,  wrought-iron  tube,  which  was  then  rifled.  Chapter 
XIX. 

These  tubes,  first  made  by  coiling  as  above  described,  were 
ultimately  replaced  by  those  of  solid  steel,  the  intrinsic 
strength  of  which  was  almost  sufficient. 

The  wrought-iron  tube  was  at  fiist  inserted  from  the  muzzle ; 
but,  as  it  was  liable  to  be  carried  out  with  the  projectile,  a 
stronger  but  much  more  costly  breech  insertion  was  employed. 

With  steel,  which  presented  no  false  welds  for  the  action 
of  the  powder  gases,  the  muzzle  insertion  was  resumed. 

In  this  way  many  10  inch  smooth-bore  Rodman  guns  were 
altered  to  8  inch  rifles.  The  15  inch  Rodman  guns  are  re- 
tained unchanged  for  subordinate  purposes. 

Foreign  Services. 

Abroad  a  similar  course  was  followed.  In  France^  the  old 
cast-iron  guns  were  hooped  with  puddled  steel,  originally  to 
retain  the  fragments  on  explosion.  The  bores  were  lined 
with  a  short  steel  tube.  This  method  is  now  followed  for 
subordinate  pieces  of  large  caliber. 

Engla7id  tried  the  Palliser  plan  of  conversion  for  her  old 
guns.  For  new  guns  wrought  iron  was  at  first  exclusively 
employed ;  then  wrought  iron  coils  on  a  steel  tube  were  used, 


XXI. — VARIETIES   OF   CANNON. 


and  finally  with  breech  loaders  steel  throughout.  The  fear 
of  the  brittleness  of  steel,  the  consequent  preference  for  the 
weaker  though  more  ductile  wrought  iron,  and  the  indiffer- 
ence to  the  molecular  treatment  of  steel  as  practiced  by  their 
more  exact  neighbors,  the  French,  have  cost  the  English 
Government  much  loss  in  time  and  money. 

To  Krupp,  in  Germany,  belongs  the  credit  of  first  using 
steel  in  large  masses.  The  weight  of  his  ingots  has  increased 
since  1851  from  two  tons  to  seventy. 

The  construction  of  his  cannon  now  requires  relatively 
large  units  of  construction.  The  tendency  elsewhere  is  to 
reduce  the  weight  of  the  maximum  unit  so  as  to  avoid  the 
large  outlay  for  plant  required  only  for  its  manufacture  and 
handling.  For  it  must  be  remembered  that  although  cannon 
comprise  the  heaviest  masses  now  made,  yet  their  commercial 
importance  is  relatively  small.     Chapter  XIV,  page  2. 

II.  BREECH  LOADING  CANNON. 

These  may  be  classified  according  to  the  means  by  which 
the  breech  is  closed  ;  but,  as  this  depends  largely  upon  the 
form  of  gas  check  employed,  this  will  be  first  discussed. 

1.  Gas  Checks. 

Many  early  efforts  were  made  to  prevent  the  escape  of  gas 
by  some  rigid  fastening  after  the  manner  of  a  plug ;  but,  owing 
to  the  erosion  through  the  slightest  crevice  caused  by  dust, 
rust  or  fouling,  the  efficiency  of  these  devices  was  short-lived. 

The  self-sealing  gas  check  alone  made  breech  loading  prac- 
ticable. Gas  checks  may  be  classified  according  as  they  are 
attached  to  or  detached  from  the  breech  block. 

Detached  Gas   Checks. 
The  ordinary  metallic  cartridge  case  is  the  best  example  of 
this  class.     The  flexibility  of  its  walls  and  its  renewal  at  every 
fire  peculiarly  adapt  it  for  this  purpose. 


XXI, — VARIETIES   OF   CANNON^ 


But,  since  it  would  be  impracticable  to  use  cartridges  of 
the  size  required  for  heavy  cannon,  the  cartridge  case  may  be 
replaced  by  a  short  permanent  ring  as  shown  in  figure  1. 

This  represents  one  form  of  an  American  invention,  the 
Broadwell  ring,  r,  with  its  obturator  plate,  /. 

The  gaseous  pressure  expands  the  thin  edge  laterally 
against  the  seat  in  the  tube  and  also  presses  the  ring  bodily 
backward  against  the  plate.  The  annular  grooves,  g,  in  the 
base  of  the  ring  serve  as  air  packing  ;  they  also  increase  the 
intensity  of  the  pressure  on  a  vital  surface,  and,  with  the  hol- 
low, h,  collect  any  fouUng,  which  might  otherwise  occur  on 
this  surface. 

The  surface^  s,  is  spherical  so  as  to  adjust  itself  easily  to  he 
spherical  seat  of  the  ring  around  the  mouth  of  the  chamber, 
past  which  the  obturator  plate  is  caused  to  slide  by  the  motion 
of  the  breech  block  to  which  it  is  attached. 

This  form  of  gas  check  is  difficult  to  maintain,  as  it  is  diffi- 
cult to  prevent  entirely  the  escape  of  gas  between  the  ring 
and  the  plate. 

Attached  Gas  Checks, 

These  necessarily  require  some  motion  of  the  block  in  the 
direction  of  the  axis  of  the  piece  and  across  the  joint  to  be 
sealed. 

Figure  2  represents  the  Freyre  gas  check  of  Spanish  origin. 
It  consists  of  a  steel  ring,  r,  of  triangular  cross-section  sur- 
rounding a  conical  wedge,  w.  This  last  is  formed  with  a 
spindle,  5,  passing  axially  through  the  breech  block,  B,  The 
stem  is  surrounded  by  a  spiral  spring  against  which  it  acts  by 
a  shoulder.  The  thickness  of  the  wedge  is  slightly  less  than 
that  of  the  ring. 

The  gases  press  the  wedge  backward  and  thus  expand  the 
ring ;  when  they  cease  to  act  the  spring  moves  the  wedge 
forward  and  thus  prevents  the  ring  from  sticking  in  its  seat. 

Figure  3  represents  the  De  Bange  (French)  gas  check,  de- 


XXI. — VARIETIES   OF   CANNON 


rived  from  that  used  in  the  Chassepot  b  1,  rifle,  a  small  arm 
firing  a  non-metallic  cartridge  The  steel  ring  of  figure  2  is 
replaced  by  a  plastic  ring,  r,  composed  of  a  mixture  of  asbes- 
tos and  tallow  enclosed  in  canvass  and  having  the  joints 
through  which  the  composition  might  extrude  protected  by- 
metallic  rings.  When  the  mushroom  head,  h,  is  compressed 
axially  the  ring,  r,  expands  laterally,  giving  a  pressure  per 

unit  of  area  against  the  surface  of  its  seat  nearly  equal  to  ^^-i- ; 

in  which  R  is  the  common  external  radius  of  the  head  and 
ring,  and  /  is  the  length  of  its  bearing. 

A  nut  on  the  rear  end  of  the  spindle  regulates  the  initial 
compression  required  for  efficiency.  A  spring  beneath  the 
nut  relieves  it  from  shock  as  the  head  is  thrown  forward  after 
firing  by  the  elasticity  of  the  tallow. 

^  Comparison. 

The  Broadwell  ring  has  to  seal  four  surfaces  not  protected 
from  dirt  instead  of  but  two,  and  the  joint,  most  difficult  to 
seal,  is  that  which  is  most  exposed  to  dirt. 

Of  the  attached  gas  checks,  the  Freyre,  being  inorganic,  is 
less  subject  to  extreme  variations  of  temperature ;  it  also  takes 
up  less  room  in  the  thickest  part  of  the  gun.  It  is  open  to 
objection  that  a  sHght  nick  on  the  edge  of  the  ring  might 
render  the  entire  apparatus  worthless. 

To  the  last  consideration  is  due  the  almost  universal 
employment  of  the  De  Bange  gas  check,  since  this  has  been 
found  almost  indestructible  by  the  accidents  of  service  and  to 
resume  its  shape  when  deformed  in  firing. 

2.  Fermeture. 

The  fermeture  (French,  fermer  to  close)  is  the  device  by 
which  the  breech  is  opened  and  closed.  Its  principal  requi- 
sites are  safety  and  convenience.  The  form  of  fermeture 
depends  largely  upon  the  kind  of  gas  check  employed. 


XXI. — VARIETIES    OF    CANNON. 


Two  principal  varieties  exist,  the  Krupp  and  the  French 
systems. 

1.  The  Krupp  or  wedge  system,  figure  4. 

Description. 

The  breech  block,  B^  moves  transversely  through  a  hori- 
zontal slot  in  rear  of  the  chamber.  The  front  face  of  the 
block  is  flat,  and  the  rear  surface  a  convex  semi-cylinder  whose 
axis  is  slightly  inclined  to  the  plane  of  the  face.  This  avoids 
the  sharp  reentrant  angles  noted.  Chapter  XV,  page  21.  It 
has  been  found  expedient  also  to  round  the  angles  in  front 
of  the  slot. 

The  upper  and  lower  surfaces  of  the  slot  contain  guides,  ^, 
which  are  parallel  to  the  elements  of  the  cylindrical  surface 
and  enter  corresponding  grooves  in  the  block.  The  block 
thus  receives  a  component  longitudinal  motion  in  the  direc- 
tion of  the  axis  of  the  bore  which  prevents  friction  between 
the  ring  and  the  obturator  plate,  and  also  assists  somewhat  in 
pressing  the  cartridge  home. 

A  hole,  h,  through  the  block  permits  the  gun  to  be  loaded 
when  the  block  is  withdrawn  to  the  proper  position.  It  is 
prevented  from  passing  this  point  by  a  stop  bolt,  screwed 
through  the  body  of  the  gun  and  having  a  blank  end  pro- 
jecting into  a  groove  on  the  upper  surface  of  the  block. 

Locking. 

To  secure  the  fermeture  a  revolving  latch^  /,  is  employed. 
For  small  cannon  using  metallic  ammunition  this  may  be  a 
simple  turn-button  operated  by  an  exterior  handle,  (9,  and 
entering  a  recess  in  one  of  the  faces  of  the  slot. 

With  a  less  perfect  gas  check,  means  must  be  provided  for 
pressing  the  obturator  plate,  /,  against  the  ring,  r,  so  that 
for  larger  guns  the  latch  consists  of  a  screw.  In  order  to 
faciUtate  the  operation  of  the  fermeture,  the  fillets  on  one 


10  XXI. — VARIETIES   OF    CANNON. 

side  of  the  newel  of  the  screw  are  removed  so  that  a  half- 
turn  of  the  screw  may  engage  or  disengage  the  remaining 
fillets. 

Translation. 

For  field  pieces  the  block  is  withdrawn  directly  by  hand, 
but  heavy  pieces  are  provided  with  a  long  screw,  S^  con- 
tained in  a  groove  in  the  upper  part  of  the  block,  and  turn- 
ing in  two  cylindrical  collars,  one  at  each  end.  The  rotation 
of  this  screw  in  a  half  nut  which  is  attached  to  the  gun, 
causes  relative  motion  to  occur  between  the  block  and  the 
gun. 

Since  for  this  motion  speed  is  required,  the  screw  is  cut 
with  a  considerable  pitch.  As  this  causes  a  loss  of  the  power 
required  to  start  the  block  from  its  seat  and  to  close  it  firmly, 
there  is  supplied  an  auxiliary  locking  screw,  d^  which  passes 
through  the  latch,  /.  By  a  peculiar  arrangement  illustrated 
in  a  model  in  the  Ordnance  Museum,  in  closing  the  breech 
this  screw  first  turns  the  latch  and  then  by  its  slow  pitch 
supplies  the  power  required,  and  conversely  in  opening. 

Both  screws  are  operated  by  a  T  wrench,  G,  which  is 
detached. 

2.  The  interrupted  screw  fermeture  is  commonly 
known  as  the  French  system,  although  its  origin  is  probably 
American. 

Description. 

A  cylindrical  block  fills  the  breech  in  the  prolongation  of 
the  bore  and  in  rear  of  the  tube. 

The  block  is  held  by  a  screw  thread  which  engages  with 
the  base  ring ;  this  in  turn  is  screwed  to  the  jacket  by  a 
ratchet  screw  thread,  Chapter  XV,  figure  47,  and  figures  2,  3 
and  10,  Chapter  XXI. 

To  facilitate  its  operation,  alternate  sections,  ordinarily  of 


XXI. — VARIETIES   OF    CANNON.  11 

60",  are  removed  from  the  adjacent  surfaces  of  the  block  and 
base  ring,  so  that  after  sUding  the  block  nearly  into  place  it 
may  be  easily  locked. 

Some  device  is  required  to  support  the  block  when  with- 
drawn.    For  small  pieces  this  is  supplied  by  the  carrier  ring. 

This  ring  is  provided  with  two  lugs  forming,  with  corre- 
sponding cavities  in  the  jacket  and  a  vertical  pin,  a  hinge  on 
which  it  swings  to  the  left  and  rear  in  opening. 

A  stop^  a  b^  Chapter  XV,  figure  47,  screwed  to  the  carrier 
ring,  enters  a  groove  formed  in  one  of  the  smooth  sectors  of 
the  block.  This  groove  terminates  in  front  at  a  short  dis- 
tance from  the  face  of  the  block,  and  in  rear  makes  a  return 
of  60°  parallel  to  the  screw  thread. 

The  carrier  ring  also  contains  a  shallow  groove,  c  d,  for 
the  head  of  the  lever,  and  the  latch,  /,  the  action  of  which  is 
important.     See  figure  10. 

The  latch  is  pressed  by  a  spiral  spring  radially  inward 
against  the  block,  so  that  its  inner  extremity  describes  on  the 
smooth  sector  on  which  it  rests  a  path  parallel  to  the  groove 
in  which  travels  the  stop.  We  will  designate  the  rearmost 
end  of  this  path  by  r,  and  the  front  end  by  /.  At  r  and  / 
are  formed  cavities  into  which  the  inner  end  of  the  latch  may 
enter  sufficiently  to  sink  its  outer  end  to  the  level  of  the  outer 
edge  of  the  carrier  ring.  Each  cavity  is  connected  with  the 
intervening  path  by  an  inclined  plane  ;  the  cavity  at  /  is  prac- 
tically a  cylinder. 

On  the  rear  face  of  the  base  ring  is  a  conical  dowel,  the 
point  of  which,  when  the  carrier  ring  is  closed,  enters  a  corre- 
sponding cavity  in  the  adjacent  face  of  the  carrier  ring. 
After  passing  this  cavity,  the  point  of  the  dowel  enters  a 
conical  hole  in  the  front  surface  of  the  latch,  and  thus  serves 
to  press  it  radially  outward,  so  that  when  the  carrier  ring  has 
been  completely  closed,  the  inner  end  of  the  latch  will  have 
been  raised  so  far  out  of  the  cavity  /  that  the  block  may  slide 


12  XXI. VARIETIES    OF    CANNON. 

freely  through  the  carrier  ring.     As  it  slides   it   forces   the 
outer  end  of  the  latch  into  its  seat  in  the  jacket. 

There  are  three  concentric  pieces,  the  block,  the  carrier 
ring  and  the  jacket.  The  latch  unites  these  alternately  in 
pairs. 

Operation. 

Suppose  the  block  to  be  closed  and  locked.  Raise  the 
lever  and  turn  the  block  to  the  left  until  the  stop  prevents 
further  rotation. 

In  so  doing,  the  inner  end  of  the  latch  rides  up  the  inclined 
plane  leading  from  r,  and  the  outer  end  enters  the  jacket  as 
shown  in  the  end  view  of  figure  47,  Chapter  XV.  This  pre- 
vents the  obstruction  to  the  withdrawal  of  the  block  caused 
by  the  simultaneous  swinging  of  the  ring  which  would  other- 
wise occur. 

The  block  can  now  ordinarily  be  freely  withdrawn ;  but  if, 
from  the  expansion  of  the  gas  check,  it  should  not  move 
freely,  an  eccentric  projection  on  the  head  of  the  lever  acts 
as  a  cam''^  and  starts  the  block  from  its  seat. 

It  is  well  to  observe  that  the  rotation  of  the  block  being 
independent  of  that  of  the  gas  check,  the  binding  of  the 
latter  does  not 'resist  the  initial  rotation  above  described. 

On  withdrawing  the  block  to  the  extent  allowed  by  the 
stop  grove,  the  inner  end  of  the  latch  drops  into  the  cavity 
f ;  the  carrier  ring  is  then  free  to  swing  in  continuation  of 
the  motion  of  withdrawal. 

After  loading,  these  motions  are  reversed.  In  closing  the 
breech  the  latch  locks  the  block  and  carrier  ring  together, 
since  any  slippipg  of  the  block  through  the  ring  would  cause 
the  edge  of  the  gas  check  to  strike  against  the  base  ring. 
This  would  be  particulariy  objectionable  in  the  Freyre  check. 

When  the  carrier  ring  comes  against  the  rear  face  of  the 


*  See  Webster. 


XXI. — VARIETIES   OF   CANNON.  IB 

base  ring  the  conical  pin  described  lifts  the  pin  from  the  hole, 
/,  and  permits  the  block  to  slide  forward  until  ready  to  en- 
gage with  the  threads  in  the  base  ring. 

After  closing  the  breech  the  eccentric  head  of  the  lever 
enters  the  groove,  c  d ;  this  prevents  the  unscrewing  of  the 
block  by  the  tangential  component  of  the  pressure  on  the 
screw  threads.  This  pressure  is  so  great  that  it  has  been 
found  necessary  to  protect  the  bearing  surface  of  the  groove, 
^^,  by  a  plate  of  hardened  steel.* 

Variations, 

For  large  pieces  a  more  stable  support  than  that  offered  by 
the  thin  carrier  ring  is  required  during  the  withdrawal  of  the 
block. 

This  is  furnished  by  a  tray  which  supports  it  for  its  whole 
length. 

This  tray  is  supported  by  a  hinge  bracket,  called  the  coit- 
sole,  which,  being  fastened  to  the  face  of  the  breech,  allows 
the  block  and  tray  to  be  swung  aside. 

For  such  pieces  the  simple  lever  used  in  the  field  piece 
affords  insufficient  power. 

It  is  accordingly  replaced  by  more  or  less  complicated 
machinery  which,  for  the  largest  calibers,  may  be  operated  by 
steam,  hydraulic  or  electrical  power. 

One  of  the  most  ingenious  devices  is  that  of  the  French 
engineer,  Canet,  who  has  an  apparatus  in  which  the  contin- 
uous rotation  of  a  crank  performs  all  the  varied  operations 
of  unlocking,  withdrawing  and  swinging  the  block. 

Vent. 
The  system  adapts  itself  to  the  use  of  an  axial  vent  which 
facilitates   ignition.     To  permit  renewal,  the  vent  piece  is 

*  The  latest  model  (1890)  exhibits  slight  changes  in  the  details  of  the 
construction  shown  in  figure  47,  Chapter  XV. 


14  XXI. — VARIETIES   OF   CANNON. 


made  removable  ;  and  to  avoid  erosion,  its  front  portion  is 
of  copper. 

To  avoid  the  danger  of  a  premature  discharge,  the  vent  is 
preferably  protected  by  a  sliding  shutter,  a  projection  from 
which  travels  in  a  concentric  groove  in  the  rear  face  of  the 
piece  which  is  so  formed  that  the  primer  cannot  be  inserted 
until  the  block  is  securely  locked  in  place. 

The  complication  attending  the  operation  of  an  axial  vent, 
the  likelihood  of  accident  to  the  gunners  from  the  projection 
of  the  fragments  of  the  ordinary  primer  and  the  necessary 
delicacy  of  the  safety  shutter  when  made  on  the  small  scale 
required  for  the  field  gun  have  so  far  caused  these  guns  to  be 
provided  with  a  radial  vent  piece  of  copper  leading  to  the  top 
of  the  charge  at  about  half  its  length. 

Base  Ring. 

The  seat  of  the  block  is  of  somewhat  greater  diameter  than 
that  required  for  loading  in  order  to  give  a  large  bearing  sur- 
face to  the  threads  of  the  screw. 

Under  Barlow's  law,  this  surface  is  less  dilated  by  the  gas 
pressure  than  one  nearer  to  the  axis ;  and,  since  from  a  simi- 
lar reason  the  greatest  stress  is  borne  by  the  foremost  fillets, 
these  do  not  approach  as  closely  to  the  end  of  the  tube  as 
the  construction  might  otherwise  permit. 

All  exposed  screw  threads  have  their  angles  rounded,  to 
avoid  fracture  and  to  resist  deformation  by  the  projectile  in 
loading.  For  heavy  pieces  a  loading  tray  is  slipped  into  the 
opening  so  as  to  cover  the  thread  in  the  base  screw  while  the 
projectile  is  being  pressed  home. 

The  operation  of  the  gun  is  very  much  facilitated  by  de- 
vices which  avoid  the  translation  of  the  breech  block.  One 
of  these  consists  in  giving  the  breech  block  a  general  conical 
shape  so  that  it  will  swing  directly  into  the  position  for 
locking. 


XXI. — VARIETIES   OF    CANNON.  16 

The  same  end  is  accomplished  in  the  Gerdon  fermeture, 
figure  13,  now  on  trial  in  the  United  States.  After  revolving 
the  block  through  90°  so  as  to  clear  the  two  threaded  sectors, 
it  is  swung  to  one  side  through  a  slot  cut  in  the  jacket.  A 
radial  slide  on  the  rear  face  of  the  block  acts  both  as  a  latch 
and  as  a  shutter  to  the  axial  vent. 

The  parts  are  remarkably  few  and  simple. 

Comparison  of  the  Two  Systems. 

1.  Except  where  metallic  ammunition  is  employed  the 
French  system  permits  the  use  of  the  best  gas  check. 

2.  It  diminishes  the  weight  of  the  gun  for  a  given  value 
of  u  and  d.     Chapter  XII. 

3.  It  serves  to  press  the  cartridge  into  place  instead  of 
guillotining  it  as  in  the  Krupp. 

4.  The  fermeture,  when  open,  is  less  exposed  to  injury 
from  a  front  fire. 

5.  It  may  be  worked  by  power. 

The  Krupp  system  in  its  conception  is  of  almost  rustic 
simplicity. 

This  advantage  is  counterbalanced  by  the  inferior  gas 
check  which  is  required  when  non-metallic  ammunition  is 
employed  ;  also  by  the  thickness  and  mass  of  the  forging 
containing  the  slot,  the  presence  of  which  must  cause  inju- 
rious internal  strain  in  oil  hardening. 

The  jar  in  opening  it  suddenly  may  deform  and  even  bend 
the  stop  bolt.  The  parts  are  less  securely  protected  in  travell- 
ing. It  has  also  the  comparative  disadvantages  named  in  the 
discussion  of  the  French  system.  The  danger  of  premature 
discharge,  though  not  so  great  as  in  the  French  system,  is  still 
said  to  exist. 


16  XXI. — VARIETIES    OF    CANNON. 


U.  S.  SYSTEM  OF  ARTILLERY. 

MOUNTAIN    SERVICE. 

The  Hotchkiss  1.65-inch  Rifle. 

This  gun  weight  but  a  Httle  over  100  pounds  and  its  car- 
riage about  twice  as  much,  so  that  either  makes  but  a  fair  load 
for  a  mule.  Metallic  ammunition  is  employed >  The  gun  is 
a  single  piece  of  steel  provided  with  the  simplest  form  of 
Krupp  fermeture  as  shown  in  figure  5  The  operation  of  the 
fermeture  can  be  readily  seen  from  the  figure  and  from  pre- 
vious discussions. 

Its  special  feature  is  the  extractor,  x.  This  is  a  prismatic 
bolt,  a  hook  on  the  front  end  of  which  engages  with  the 
flange  of  the  cartridge  (Chapter  XVI,  figures  8  and  9)  as  this 
is  loaded 

The  extractor  slides  in  a  longitudinal  groove,  g,  on  the 
upper  surface  of  the  slot  On  its  lower  face  is  a  tenon  which 
enters  a  transverse  groove,  g' ,  in  the  upper  face  of  the  block. 

The  groove,  g' ^  near  the  handle  is  straight  and  slightly 
inclined  to  the  rear  face,  so  as  to  give  power  in  wedging  the 
cartridge  case  from  its  seat.  The  screw  thread  on  the  latch 
also  assists.  At  the  other  end  it  is  so  curved  that  when,  in 
opening  the  breech,  the  loading  hole  comes  opposite  to  the 
chamber  the  extractor  will  be  suddenly  drawn  backwards, 
throwing  the  free  cartridge  case  clear  of  the  gun.  The  first 
of  these  operations  is  called  the  extraction,  and  the  second 
the  ejection 

For  simplicity  this  piece  is  fired  with  the  ordinary  friction 
primer.  The  blast  from  this  raises  the  central  portion  of  a 
thin,  cup-shaped  gas  check  within  the  cartridge,  and  the 
flame  passes  through  the  three  holes  shown  in  figure  8,  Chap- 
ter XVI.  As  soon  as  the  charge  is  ignited  the  back  pres- 
sure of  the  gases  closes  the  vent  by  reversing  the  action  of 
the  gas  check, 


XXI. — VARIETIES   OF   CANNON.  17 


Hotchkiss  3-Inch  Mountain  Rifle. 

In  order  to  permit  the  use  of  shrapnel  a  heavier  mountain 
gun  of  3-inch  caUber  has  been  recently  produced.  Figure  11. 

Foreign   Variations, 
In   order  to  increase  both  the  power  and  portability   of 
mountain  cannon  they  are  frequently  made  abroad  in  sections 
which  are  screwed  together  before  firing.     "  Screw-guns  "  of 
8-inch  caliber  have  been  successfully  fired . 

FIELD    SERVICE. 

The  3.2  B.  L.  Rifle  shown  in  Chapter  XV,  figure  47,  is 
the  only  new  field  piece  now  issued.  (1891.)  It  is  eventu- 
ally intended  for  use  as  a  Horse  Artillery  gun,  and  to  be 
replaced  for  Field  Service  proper  by  a  similar  gun  of  3.6 
in  caliber,  firing  a  20-pound  shell.  A  3.6  B.  L.  Mortar, 
figure  12,  firing  the  same  projectile,  is  also  contemplated  for 
delivering  vertical  fire  against  troops  sheltered  by  temporary 
defences.     It  has  a  range  of  nearly  two  miles. 

Foreign    Variations. 
It  is  proposed  in  France  to  have  but  one  caliber,  about 
3  in.  for  all  mountain    and  field   service,  viz.,  short,  light, 
long  and  heavy  pieces. 

SIEGE    SERVICE. 

Siege  cannon  are  intended  for  attacking  and  defending 
inland  fortifications  and  the  land  fronts  of  sea- coast  fortifi- 
cations. 

The  term  is  usually  applied  to  pieces  which,  although  too 
heavy  for  field  operations,  are  yet  light  enough  to  be  trans- 
ported over  common  roads  upon  the  carriages  from  which 
they  are  fired. 

This  limits  the  weight  of  the  gun  and  carriage  together  to 
that  which  may  safely  be  transported  across  a  pontoon  bridge. 


18  XXI. VARIETIES   OF   CANNON. 

Siege  Gun. 

The  5-inch  siege  rifle,  figure  6,  resembles  in  its  construction 
the  field  gun  described. 

Siege  Howitzer. 

Principles  of  Design, 

Defences  of  masonry  have  been  largely  replaced  by  those 
which  are  armored,  or,  particularly  for  the  besieging  party, 
of  earth. 

While  armor  requires  for  its  penetration  the  concentration 
of  kinetic  energy  found  in  a  projectile  of  relatively  small 
diameter  fired  from  a  gun,  the  demolition  of  earth  works 
demands  rather  the  transfer  of  energy  in  the  potential  form. 
Such  defences  should  therefore  be  attacked  by  cannon  of 
the  largest  caliber  consistent  with  portability. 

If  the  maximum  weight  of  the  piece  is  fixed  by  the  con- 
siderations previously  named,  then  by  the  definition  of 
Chapter  I,  a  howitzer  results. 

The  proportions  of  this  piece  are  also  demanded  by  the 
advantages  pertaining  to  vertical  fire  againt  the  large  and 
well  defined  area  occupied  by  the  besieged,  against  com- 
munications of  the  besieger  which  are  screened  from  view, 
and  against  the  roofs  of  turrets.  The  shorter  the  piece  is 
in  rear  of  the  trunnions  the  more  easily  may  high  angles 
of  fire  from  a  given  carriage  provided  with  the  ordinary 
elevating  screw  be  attained.*  The  avoidance  of  preponder- 
ance and  the  requisite  strength  of  the  chase  demand  that 
the  length  in  front  of  the  trunnions  be  also  reduced. 

Such  considerations  have  fixed  the  value  of  u  at  about 
12  times  the  caliber,  which  is  7  inches. 

It  is  intended  to  throw  a  projectile  weighing  about  100 
pounds  to  a  distance  of  about  3  miles. 

*A  new  German  howitzer  has  the  trunnions  placed  ahuost  at  the  breech. 
In  this  carriage  the  elevating  screw  is  under  the  chase,  as  the  arrange- 
ment adopted  gives  a  considerable  muzzle  preponderance.  See  also  Car- 
riage for  7-inch  Howitzer,  Chapter  XXIII,  figure  6. 


XXK — VARIETIES   OF   CANNON.  19 


Owing  to  the  strength  of  the  construction  a  larger  cahber 
might  have  been  employed  for  the  given  weight,  but  in  such 
a  case  the  energy. of  recoil,  (Equation  7,  Chapter  XIX,) 
would  have  been  excessive. 

Since  with  the  value  of  /„  usual  in  built  up  steel  guns,  the 
short  length  of  bore  reduces  the  value  of  e^  it  is  proposed  to 
utilize  the  value  of  E  permitted  by  the  strength  of  the  car- 
riage by  increasing  the  value  of  ;//. 

This  will  permit  the  use  of  very  long  torpedo  shells 
(Chapter  XVI,  page  20).  The  limit  of  E  for  the  wheeled 
carriage  having  thus  been  reached,  for  high  angles  of  fire 
which  increase  the  stress  upon  the  axle,  E  may  be  further 
increased  by  dismounting  the  wheels  and  laying  the  stock  of 
the  carriage  on  a  platform  It  is  now  (1891)  proposed  to  use 
in  the  field  service  a  6  inch  B.  L  mortar  throwing  a  70 
pound  shell,  to  be  mounted  as  above  described 

It  is  probable  that  in  the  future  the  obstruction  to  effi- 
ciency which  is  due  to  the  requirement  that  the  piece  be 
transported  on  the  carriage  from  which  it  is  to  be  fired,  will 
disappear  before  the  adoption  of  special  carriages  designed 
with  the  view  of  efficiently  satisfying  their  independent 
requirements. 

Charges. 

In  order  to  vary  the  angle  of  fall*  to  suit  the  range  and 
the  kind  of  fire  employed,  the  howitzer  is  fired  with  varying 
charges  of  powder  as  well  as  with  varying  angles  of  fire.  In 
this  it  differs  from  the  gun  in  which  the  charge  is  usually  a 
constant  and  a  maximum.     See  Chapter  XXX,  page  9. 

7-Iiich  B.  L  Howitzer 

The  construction,  figure  8,  resembles  that  of  the  field  piece, 
the  principal  difference  being  in  the  construction  of  the  key 
ring.     This  consists  of  two  semi-circular  segments    of  rect- 

*The  angle  with  the  horizontal  made  by  the  tangent  to  the  trajectory 
on  impact. 


20  XXI. — VARIETIES   OF   CANNON. 

angular  cross-section  which  are  laid  in  a  shallow  groove  in 
the  tube  so  as  to  project  above  its  exterior  and  to  bear 
against  the  front  face  of  the  trunnion  hoop.  They  are  kept 
in  place  by  the  lap  of  the  sleeve. 

The  friction  developed  by  shrinkage  between  the  jacket 
and  the  tube  throws  part  of  the  longitudinal  stress  upon  the 
tube  from  which  the  key  ring  transfers  this  stress  to  the 
trunnions. 

A  shoulder  formed  on  the  tube  in  rear  prevents  the  for- 
ward motion  of  the  tube  from  the  friction  between  it  and  the 
projectile.     See  page  5.     This  feature  is  general, 

The  cavities  in  the  ends  of  the  trunnions  are  for  the  points 
of  the  bailm  which  the  piece  is  slung  in  mounting. 

SEA    COAST    CANNON. 

These  comprise   rifles  of  and    above  8-inch  caliber,  and 
12-inch  rifled  mortars, 
Eifles. 

Figure  7  shows  the  8-inch  b  1.  steel  gun  with  which  most 
of  the  recent  experiments  have  been  made. 

The  construction  resembles  that  heretofore  discussed, 
except  that  the  jacket  is  strengthened  by  two  rows  of  hoops, 
which  since  the  original  design,  have  been  extended  to  the 
muzzle.     (Chapter  XI,  page  18,  paragraph  4.) 

Other  S.    C,  Rifles. 

The  guns  so  far  designed  are  of  8,  10,  12  and  16-inch 
caliber.  Being  intended  for  use  with  the  largest  charges  of 
slow  burning  powder,  they  are  made  very  long,  the  values  of 
u  ranging  from  about  24  to  27  calibers. 

For  the  largest  calibers  it  is  proposed  to  dispense  with 
trunnions  which  are  to  be  replaced  by  several  rows  of  cir- 
cumferential ribs,  by  which,  as  in  cannon  of  the  very  earliest 
iimeSy  the  pieces  are  to  be  secured  to  their  support.  The 
necessary  alterations  in  elevation  will  be  given  by  varying  the 


XXI. — VARIETIES   OF    CANNON.  21 

inclination  of  the  chassis,  to  which  by  this  arrangement  the 
recoil  is  always  parallel. 

Mortars. 

The  importance  of  nearly  vertical  impact  against  the 
decks  of  vessels  at  short  ranges  requires  the  mortars  to  fire 
with  angles  of  elevation  as  great  as  75°. 

It  is  proposed  to  group  them  in  sunken  batteries  of  12  or 
16  mortars,  united  under  the  control  of  one  officer.  He  will 
occupy  a  detached  position  free  from  smoke,  and  will  be  pro- 
vided with  an  accurate  range  finder,  and  with  means  of  com- 
municating to  the  chiefs  of  pieces  the  direction  and  elevation 
required.  A  simultaneous  volley  from  the  battery  will  prob- 
ably drive  from  its  anchorage  any  vessel  within  range.  This 
will  be  an  important  aid  to  the  defense,  since,  as  the  bom- 
bardment of  Alexandria  in  1882  clearly  showed,  the  accuracy 
of  fire  from  a  vessel  is  much  diminished  when  the  vessel  is 
under  way. 

V2,-inch  B.  L.  Mortar.     {Figure  9.) 

The  immediate  supply  of  these  cannon  demanded  by  our 
present  necessities  (1891)  and  the  relatively  low  energies 
required  to  penetrate  armored  decks  by  vertical  fire  have  so 
far  permitted  the  body  of  these  pieces  to  be  made  of  iron 
cast  on  the  Rodman  principle  and  strengthened  by  two  rows 
of  steel  hoops  as  shown  in  figure  9. 

The  recent  failure  at  a  pressure  of  less  than  20,000  pounds 
of  an  unhooped  12-inch  cast  iron  mortar  would  indicate  the 
future  use  of  steel  throughout  the  piece  as  soon  as  the  steel 
works  and  the  gun  factory  shall  have  become  able  to  supply 
a  sufficient  numl)er  of  heavy  steel  guns. 

The  growing  importance  of  vertical  fire  has  caused  the 
employment  of  mortars,  even  upon  ship  board,  to  be  seriously 
considered. 

The  value  of  u  in  this  piece  is  about  6  calibers. 


22 


XXI. — VARIETIES   OF   CANNON. 


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XXII. — ARTILLERY   CARRIAGES. 


CHAPTER    XXII. 

ARTILLERY    CARRIAGES. 

PRINCIPLES    OF    CONSTRUCTION. 

Classification. 

Artillery  carriages  may  be  classified  according  as  they  are 
intended  to  support  the  piece  when  fired,  to  transport  it,  and 
to  supply  it  with  ammunition  and  accessories.  These  func- 
tions are  sometimes  combined. 

They  may  also  be  classified  according  to  the  service  in 
which  they  are  employed. 
Requisites. 

1.  Strength  to  resist  permanent  deformation  from  the  shock 
of  recoil. 

2.  Stability  in  firing  and  on  the  march. 

3.  Mobility  as  regards  the  ease  of  service  in  battery,  and 
of  transportation  when  required. 

4.  Only  a  moderate  recoil  in  firing,  so  as  to  facilitate  the 
service  of  the  piece  and  to  avoid  the  exposure  of  the  gunners 
when  sheltered  by  defences.  A  compromise  between  these 
properties  is  often  necessary. 

I.  CARRIAGES  WHICH  SUPPORT  THE  PIECE. 

GENERAL   DESCRIPTION. 

These  are  called  gun  carriages.  They  may  be  either  sta- 
tionary  or  wheeled. 

Stationary  Carriages. 

The  simplest  form  exists  in  the  iron  mortar  bed  used  for  the 
old  S.  B.  Mortars. 


X3tll. — ARTILLERY  CARRIAGES. 


This  consists  of  trapezoidal  plates  forming  the  cheeks^  which 
support  the  trunnions  of  the  piece  at  such  a  height  as  to  per- 
mit it  to  receive  the  elevation  required.  The  cheeks  are  con- 
nected by  transverse  diaphragms  called  transoms  and  bolts  in 
order  to  form  a  strong  frame.  For  heavy  pieces  each  cheek 
may  consist  of  two  plates  united  to  a  T  shaped  bar  as  shown 
in  figure  1.  The  cheeks  may  be  stiffened  in  the  direction  of 
compressive  stresses  by  bars  included  between  the  plates. 

The  bearings  of  the  trunnions  may  be  widened  by  trunnion 
bed  plates^  so  as  to  diminish  the  pressure  per  unit  of  area 
which  they  are  called  upon  to  support.  The  mortar  bed  is 
made  low  for  ease  of  loading  and  for  stability.  The  prin- 
ciples of  construction  above  noted  are  of  general  application. 

Sea  coast  gun  carriages  are  intended  to  be  used  in  firing 
over  a  parapet  or  through  an  embrasure.  In  the  first  case 
they  are  called  barbette  carriages,  and  in  the  second,  casemate 
carriages.  Owing  to  the  height  of  the  piece  above  the 
ground  and  the  low  angles  of  fire  employed,  the  stability  of 
the  system  generally  requires  the  support  of  the  piece  to  be 
divided  into  the  gun  carriage  proper,  constructed  like  the 
mortar  bed,  and  tlie  chassis,  which  is  a  moveable  railway 
capable  of  directing  the  piece  in  its  recoil  and  of  being  trav- 
ersed in  azimuth. 

Non-recoil  carriages  are  separately  treated  hereafter. 

Wheeled  Carriages. 

In  the  mountain,  field  and  siege  services,  the  gun  carriage 
must  also  be  adapted  to  transportation.  This  involves  the 
use  of  wheels,  which  complicate  the  problem  of  controlling 
the  recoil. 

Parts. 

Their  essential  parts  are  :  — 

1,  The  stock.  This  is  a  prolongation  of  the  cheeks  which, 
with  the  wheels,  forms  the  three  points  necessary  for  stability. 


XXII. — ARTILLERY   CARRIAGES, 


A  greater  number  of  supports  might  affect  the  stability  on 
uneven  ground. 

The  stock  serves  also  to  point  the  piece,  since  it  sustains 
the  elevating  screw,  and  with  the  aid  of  the  handspike  gives 
the  necessary  changes  in  azimuth 

It  also  connects  the  front  and  rear  wheels  in  transporta- 
tion. 

For  modern  carriages  the  stock  consists  of  two  sheet 
steel  flasks  or  brackets  which  rest  at  the  head  of  the  stock 
upon  the  axle,  and  are  united  at  the  further  end  by  the  trail 
plate  or  shoe, 

2.  The  wheels  and  the  axle  replace  the  continuous  support 
afforded  in  stationary  carriages  by  the  cheeks. 

PERIODS    OF   THE    RECOIL. 

The  recoil  may  be  separated  into  two  periods  : 

1,  That  during  which  the  projectile  is  acquiring  energy  in 
the  piece. 

2.  That  comprising  the  subsequent  recoil.  Since  the 
carriage  is  found  not  to  move  materially  until  the  projectile 
has  reached  the  muzzle,  and  since  the  system  is  not  rigid, 
the  corresponding  phenomena  may  be  taken  to  be : 

1.  A  series  of  shocks  between  the  trunnions  and  their 
beds  transmitted  through  the  axles  to  the  wheels  and  through 
the  stock  to  the  trail.  The  system  is  finally  set  in  motion  by 
these  shocks. 

2.  The  resulting  motion  of  the  system  accelerated  by  the 
remaining  gaseous  pressure  and  retarded  by  friction  and 
various  artificial  resistances. 

Energy  of  Recoil. 

The  nature  of  the  recoil  is  preferably  studied  by  veloci- 
meters  of  Class  III.  But,  as  this  is  difficult  and  requires  the 
previous  construction  of  the  carriage,  it  is  customary  for 
theoretical  discussions  of  a  general  nature  to  ignore  the  first 


XXII — ARTILLERY   CARRIAGES. 


period,  and  to  assume  that  the  system  is  rigid  and  that  the 
acceleration  to  the  system  during  the  second  period  is  com- 
pensated for  by  the  acceleration  of  the  projectile  noted  in 
Chapter  XI,  page  18.* 

We  may  therefore  change  Equation  (7),  Chapter  XIX, 
to  read 

in  which  the  subscript  s  refers  to  the  entire  system  recoiling. 
For  greater  accuracy,  when  the  mass  of  the  powder,  or 
m'^  bears  a  considerable  ratio  to  that  of  the  projectile,  we 
may  use  the  following  formula  in  which  v'  represents  the 
mean  velocity  of  the  products  of  combustion,  found  by 
experiment  to  be  about  3,000  /.  s. 

_  m  V  +  m'  v' 

Distribution  of  "Work  of  Eecoil. 

Since  this  work  is  distributed  between  the  two  periods, 
and  since  it  is  necessary  to  restrict  the  exent  of  the  recoil,  it 
becomes  necessary,  as  in  Chapter  V,  to  determine  the 
maximum  stress  which  the  system  can  safely  endure  and  to 
maintain  this  stress  as  nearly  constant  as  possible  over  the 
path  of  the  recoil. 

This  principle,  which  underlies  all  recent  improvements,  in 
gun  carriages,  owes  its  importance  to  the  recent  increase  of 
m  and  e  and  the  decrease  m  M  (Equation  7,  Chapter  XIX), 
due  to  the  general  use  of  built  up  rifled  cannon  firing  large 
charges  o^ progressive  powder  In  fact,  it  may  be  said  that 
the  limit  of  the  power  of  cannon,  or  h,  page  21,  Chapter  XI, 
is  fixed  by  the  difficulty  of  controlling  their  recoil, 

If  we  assume  that  the  mobility  of  the  system  fixes  the  sum 
of  the  masses,  M  and  J/',  composing  the  gun  and  carriage, 


This  assumption  will  be  corrected  as  occasion  arises  hereafter. 


XXII. ARTILLERY    CARRIAGES. 


the  following  discussion  explains  the  prevailing  practice  of 
making  M'  approximately  equal  to  M. 

For,  if  we  assume  the  carriage  to  be  properly  proportioned, 
general  experience  shows  that  its  permanent  deformation,  Q, 
may  be  considered  inversely  proportional  to  its  mass  and 
directly  proportional  to  the  energy  which  it  receives.     So  that 

liM-{-  M'  =z  C,  Q  will  be  least  when  M  —  M'. 

The  assumption  on  which  this  deduction  is  based,  although 
confirmed  by  experience  in  the  construction  of  carriages,  an- 
vils and  armor,  is  not  conclusive ;  since  mechanical  ingenuity 
may  compensate  for  the  loss  of  strength  resulting  irom  a 
diminution  of  M' . 

REMARKS. 

It  is  found  that  with  quick  powders  the  velocity  of  recoil 
during  the  first  period  is  greater  than  with  slow  powders,  the 
maximum  momentum  of  the  projectile  being  the  same. 

With  slow  powders  the  velocity  during  the  second  period 
is  increased  to  such  an  extent  by  the  high  pressure  as  the 
projectile  leaves  the  gun  (Chapter  XI,  page  18),  that  special 
devices  have  become  necessary  to  diminish  the  increased 
extent  of  the  recoil. 

The  problem  is  so  complicated  that  computations,  princi- 
pally by  graphical  methods,  are  mainly  resorted  to  in  order 
to  determine  the  direction  of  the  stresses,  the  corresponding 
dimensions  being  found  empirically.  It  is  highly  probable 
that  the  gun  carriages  of  the  future,  like  many  other  construc- 
tions, will  be  the  outgrowth  of  practical  experience. 

FORCES  ACTING  ON  A  GUN  CARRIAGE. 

Velocity  of  Translation. 

If  the  axis  of  the  bore  intersects  the  axis  of  the  trunnions 
at  the  centre  of  gravity  of  the  piece,  the  force  producing  re- 


XXII. ARTILLERY    CARRIAGES. 


coil  is  communicated  to  the  carriage  at  the  trunnion  beds. 
The  carriage  being  constructed  symmetrically  with  regard  to 
the  axis  of  the  piece,  we  may  suppose  that  the  wheels,  trun- 
nion beds  and  trail  are  all  situated  in  the  same  plane  and  that 
the  force  producing  recoil  is  applied  at  the  point  where  the 
axis  of  the  trunnions  pierces  this  plane. 

The  direction  in  which  this  force  acts  will  be  that  given  by 
the  angle  of  fire  or  the  inclination  to  the  horizontal  of  the  axis 
of  the  piece. 

Let  V  figure  2,  be  the  position  of  the  axis  of  the  trunnions, 
and  mv-=.I,^  represent  the  intensity  and  direction  of  the 
force,  and  Q  the  angle  of  fire.  Let  Z'be  the  point  of  contact 
of  the  trail  and  ground,  /  the  distance  of  this  point  from  the 
trunnions,  and  a  the  angle  made  by  the  line  Tv,  with  the 
horizontal.  Let  W^  be  the  weight  of  the  system  acting 
through  the  center  of  gravity  G  at  the  horizontal  distance  b 
from  the  point  T.  Let/ be  the  coefficient  of  friction  between 
the  carriage  and  the  horizontal  platform  on  which  it  rests. 

The  vertical  component  of  /, ,  and  W^  will  cause  friction 
between  the  carriage  and  the  platform.  The  force  of  friction 
or/(^g  4"  '^^  ^  s^'^  ^)'  wil^  oppose  motion.  So  that,  repre- 
senting by  Fthe  horizontal  velocity  of  recoil,  we  have 

y.     m  V  cos  6  — /  ( ^8  4~  ^^^  ^  sin  B) 
m  V  (cos  0  —  /  sin  0) 

in  which  g  f  may  be  neglected. 

The  vertical  component  will  be  distributed  along  the  sup- 
ports in  a  manner  determined  by  the  construction  of  the  car- 
riage and  the  values  of  Q.  For  wheeled  carriages  /will have 
separate  values  for  the  wheels  and  the  trail. 

If,  in  Equation  4,  we  neglect  the  weight  of  the  system  in 
comparison  with  the  vertical  component  of  7, ,  (or  g  /),  we 


XXII. — ARTILLERY   CARRIAGES. 


find  that  V  will  reduce  to  0,  or  that  recoil  will  cease  for  a 
value  of  0,  such  that,  calling  this  angle  0, 

tan  e,  =  y  (5) 

This  is  called  the  angle  of  no  recoil. 

Extent  of  Recoil. 

The  extent  of  the  recoil  will  be 


s=^-^.'  (6) 


If,  as  is  usual,  the  platform  be  inclined  at  an  angle,  /3,  with 
the  horizon  so  as  to  check  the  recoil,  then  for  6  in  the  above 
equations  should  be  written 

d  +  (3;   and  for  F,  Tcos  3. 

In  this  case,  since  the  energy  of  the  recoil  is  absorbed  not 
only  by  friction  but  by  the  work  done  in  lifting  JV^  through 
a  height  =  s  sin  (3,  we  have 

Fcosfi' 


2  g  (sin  (3  +  / cos  (i) 


(J) 


These  equations  are  said  to  give  correct  values  for  stationary 
carriages,  but  do  not  apply  very  exactly  to  those  which  are 
wheeled. 

Angpilar  Velocity. 

The  force,  /, ,  also  acts  to  rotate  the  carriage  around 
the  point  T  with  a  moment  proportional  to  its  lever  arm, 
/  sin  (a — 6),  so  that  the  moment  of  this  force  will  be 
m  V  Isin  (a  —  6). 

This  is  opposed  by  the  moment  of  the  weight,  or  JV^  b. 
Then,  since  the  angular  velocity  of  the  system  is  equal  to 
the  resultant  moment  of  the  impressed  forces  divided  by  the 
moment  of  inertia  of  the  system,  we  have,  representing  the 


XXII. — ARTILLERY   CARRIAGES. 


angular  velocity,  about  T  by  o)  and  the  corresponding  radius 

of  gyration  by  k. 

mvl  sin  (a  —  Q\  —  W^  b 
--S '-j^J •-  (8) 

With  this  relation  we  may  discuss  in  an  elementary  manner 
the  stability  of  the  system.  For  example,  in  the  old  S.  B. 
Mortars,  since  W^  is  small,  a  is  made  less  than  0,  so  as  to 
make  w  negative. 

Phenomena  of  Recoil. 

Practically  the  phenomena  are  much  more  complex,  since 
the  rotation  of  the  system  is  not  immediate. 


Wheeled  Carriages. 

In  these  the  wheels  tend  to  slide  or  rise  to  an  extent 
determined  by  the  resistance  to  sliding  at  T.  Since  T  is 
not  necessarily  on  a  reciprocal  axis  of  spontaneous  rotation, 
the  stock  is  subjected  to  a  transverse  stress.  When,  after 
rotation,  the  wheels  fall,  the  axle  receives  a  shock,  and  the 
trail  being  thrown  up,  the  system  recoils  by  roUing,  and  so 
on  until  the  system  comes  to  rest. 

Rotation  during  the  first  period  tends  to  derange  the  aim 
by  what  is  called  the  angle  of  jump^     See  Chapter  XX. 

During  the  first  period,  since  the  trunnions  fit  rather 
loosely  in  their  beds,  a  frictional  moment  is  developed  on 
the  under  side  of  the  trunnions  This  causes  abnormal 
pressure  on  the  head  of  the  elevating  screw,  which,  owing 
to  the  elasticity  of  the  system,  subsequently  receives  one  or 
more  severe  blows  from  the  breech.  The  effect  is  destructive, 
since  the  bearing  of  this  screw  upon  its  nut  is  restricted,  and 
the  necessary  play  between  the  screw  and  nut  increases  the 
striking  velocity  of  the  parts. 

The  objections  may  be  mitigated  by  making  the  piece 
without  preponderance,  and  by  arranging  the  elevating  screw 
so  that  its  axis  will  be  always  normal  to  the  surface  which  it 


XXII. — ARTILLERY   CARRIAGES. 


supports,  since  this  will  avoid  the  tendency  to  bend  under 
pressure. 

Other  phenomena  also  occur. 

The  inertia  of  the  wheels  develops  in  the  axle  a  consider- 
able transverse  stress. 

In  rifled  pieces  a  rotary  moment  is  developed  which  tends 
to  raise  from  its  bed  the  trunnion  toward  which  the  top  of  the 
projectile  is  revolving,  and  thus  to  raise  one  wheel  higher 
than  the  other  as  the  system  jumps.  The  effect  will  be  to 
concentrate  most  of  the  shock  of  the  fall  upon  the  lower 
wheel. 

Stationary  Carriages. 

The  chassis  of  stationary  carriages  revolves  around  a  massive 
vertical  pintle  which  may  be  placed  in  front  of  the  chassis  or 
at  its  middle. 

While  the  former  position  is  necessary  for  pieces  firing 
through  embrasures,  in  other  cases  the  center  pintle  chassis 
is  preferred,  since  a  given  change  in  azimuth  covers  less 
ground. 

The  tendency  of  the  top  carriage  to  jump  is  restrained  by 
projections  which  engage  under  the  chassis,  but  tend  to  lift 
the  pintle  from  its  socket.  The  pintle  is  also  exposed  to  a 
horizontal  stress  nearly  equal  to  the  normal  pressure  between 
the  carriage  and  the  chassis  multiplied  by  the  sine  of  the 
inclination  of  the  chassis  to  the  horizon. 

The  strength  of  the  pintle  and  its  fastenings  is  therefore  an 
important  subject  of  consideration. 

Angle  of  Greatest  Recoil. 

Since  the  energy  of  recoil  is  distributed  between  the 
motions  of  rotation  and  translation,  the  maximum  velocity 
of  recoil  will  follow  from  an  angle  of  fire  such  that  w  =  0. 
Equation  (8)  does  not  contain  all  the  data  necessary  for  a 


10  XXIi. — ARTILLERY   CARRIAGES. 

full  discussion ;  but  it  may  be  shown  that,  if  the  weight  of 
the  system  be  neglected,  and  the  notation  of  figure  2  be 
adopted,  if  we  call  the  angle  of  greatest  recoil,  6^,  then 

Since  A'^/i,  this  value  of  B^  is  always  positive,  or  the 
maximum  velocity  of  recoil  will  follow  the  use  of  an  angle 
of  fire  ]>0.  This  value  of  6  should  therefore  be  employed 
in  all  calculations  relating  to  limiting  the  extent  of  recoil. 

The  angle  6^,  may  also  be  called  the  ang/e  of  no  rotation^ 
i.  e.  the  angle  for  which  all  the  energy  of  recoil  is  expended 
in  translation  only.  It  may  be  taken  to  measure  the  exposure 
of  the  system  to  the  injurious  shocks  resulting  from  rotation, 
since,  in  ordin-ary  firing,  Q  is  less  than  Q^^  and  therefore  rota- 
tion is  ordinarily  produced. 

Equation  9  shows  that  d^  may  be  diminished  by  the  fol- 
lowing means  : 

1.  By  making  h'  —  h  as  small  as  possible.  Owing  to  the 
length  of  a  in  stationary  carriages  this  correction  is  princi- 
pally confined  to  those  that  are  wheeled.  In  these  h'  is 
made  as  small  as  facility  of  loading  and  the  protection  of  the 
gunners  by  the  parapet  will  permit,  and  h  is  increased  by 
bringing  the  axle  as  near  to  the  trunnions  as  the  size,  strength 
and  weight  of  the  wheel  will  allow. 

2.  By  making  a  as  long  as  conditions  relating  to  mobility 
in  transportation  will  permit.  , 

3.  By  making  /small. 

In  stationary  carriages  /  is  normally  great,  and,  as  here- 
after seen,  the  resistance  to  sliding  is  generally  artificially  in- 
creased. For  these  carriages  it  is  especially  necessary  that  a 
be  made  large. 

The  stresses  developed  in  field  carriages  by  a  large  value 
of/,  as  when  the  site  is  sandy  or  the  trail  is  rested  against  a 


XXII. — ARTILLERY   CARRIAGES.  11 

rock,  are  evidently  prejudicial.  They  may  sometimes  be  in- 
evitable, as  when  firing  across  a  valley  at  a  high  mark,  since 
in  such  a  case  the  trail  may  require  sinking  into  a  hole. 

DEVICES    TO    CONTROL    RECOIL. 

These  may  be  considered  according  to  the  end  in  view, 
as  they  seek,  I,  merely  to  limit  the  path;  or,  II,  to  regulate 
the  resistance. 

It  is  generally  advisable  to  store  up  enough  of  the  work  of 
recoil  to  assist  in  bringing  the  piece  back  into  battery.  The 
return  may  be  facilitated  by  the  use  of  eccentric  rollers. 

These  devices  ar-e  often  combined  in  the  same  carriage. 

Class  I.  To  the  first  class  of  devices  belong  those  in  which 
the  energy  is  absorbed  by  friction  or  in  which  a  weight  is 
raised. 

Stationary  Carriages. 
Friction  Checks. 

This  variety  is  least  valuable  since  it  stores  up  no  useful 
work.  In  the  best  types  the  friction,  due  to  the  normal  com- 
ponent of  the  weight,  is  increased  by  the  artificial  pressure 
of  a  screw  clamp. 

The  effect  of  a  given  pressure  on  the  screw  may  be  in- 
creased by  increasing  the  number  of  surfaces  upon  which  it 
acts.  Thus,  in  Ericcson*s  compressor  we  have  7i  parallel  plates 
attached  to  the  chassis  and  alternating  between  n  -\-l  pieces 
so  attached  to  the  carriage  that  while  they  recoil  with  it,  a 
sHght  initial  play  is  allowed.  Suppose  this  play  to  be  de- 
stroyed by  a  normal  pressure  P.  We  shall  then  have  for  the 
friction  of  the  compressor  P  =:  P/ {2  n)  and  from  Equa- 
tion (7) 

(v  cos  13  y 


2g(s[nf5+/cos(3+-^j 


(10) 


12  XXII. — ARTILLERY   CARRIAGES. 

The  main  objection  to  this  system  is  the  variable  value  of 
F^  since  this  depends  upon  the  judgment  of  the  operator,  and 
upon  the  state  of  the  surfaces,  and  is  greater  for  static  friction, 
when  the  acceleration  is  greatest,  than  afterwards. 

This  arrangement  is  modified  in  the  Sinclair  check  used 
with  some  converted  U.  S.  Sea  Coast  guns. 

This  consists  essentially  of  a  clamp  embracing  a  plate  in- 
creasing slightly  in  thickness  from  front  to  rear.  To  prevent 
the  plate  from  buckling  in  consequence  of  the  counter  recoil 
produced  by  the  elasticity  of  the  parts,  the  front  end  of  the 
plate  is  free  to  move  forward  through  its  attachment  to  the 
chassis. 

Wheeled  Carriages. 

These  may  be  braked  by  various  means.  Among  these  is 
the  Hotchkiss  brake  which  consists  of  nuts  threaded  upon  the 
axles  between  the  wheels  and  serving,  by  friction  produced 
against  the  hubs  of  the  wheels,  to  keep  the  wheels  from 
turning. 

This  brake  is  an  example  of  the  friction  clutch  often  em- 
ployed in  the  transfer  of  energy.  When  the  tangential  com- 
ponent of  the  force  producing  rotation  exceeds  that  of  fric- 
tion, sliding  takes  place  and  the  destruction  of  the  resisting 
parts  is  averted. 

This  principle  is  sometimes  applied  to  the  elevating  screw, 
since  the  clutch,  which  is  required  to  vary  d  only,  will 
yield  under  the  shocks  of  recoil  and  save  the  deformation 
of  the  parts. 

A  simple  brake  may  be  extemporized  by  lashing  the 
wheels  to  the  trail  by  a  rope ;  but,  as  this  strains  the  wheel, 
a  better  way,  often  used,  is  to  rest  the  wheels  on  shoes 
attached  by  tension  to  the  trail,  as  in  wagons  of  commerce. 

The  latest  patterns  of  brake  admit  of  a  partial  distribution 
of  the  pressure,   as  explained  later  and  in  Chapter  XXIII. 


XXII. ARTILLERY    CARRIAGES.  13 


They  may  also  be  used  in  transportation  without  necessarily 
stopping  the  carriage,  as  is  required  when  the  shoe  is  used. 

Raising  a  Weight. 

If  the  piece  raise  its  own  weight,  its  exposure  is  increased ; 
while,  if  it  raise  a  counterpoise,  it  may  itself  descend.  Such 
carriages  are  called  disappeari7ig  carriages, 

Moncrieff  Carriage. — Figure  3 

In  this  the  flasks  rock  on  the  chassis  so  that  the  counter- 
poise, Wy  which  was  at  first  beneath  the  gun,  has  finally 
a  considerable  moment  of  restitution.  By  varying  the 
curvature  of  the  flasks  this  moment  may  be  made  to  vary 
inversely  with  the  acceleration  of  the  recoil  so  that  the 
stresses  between  the  piece  and  the  counterpoise  may  be 
nearly  constant.  Conversely,  the  return  to  battery  will  be 
gentle.  The  rack  and  pinion  serve  to  retain  the  piece  for 
loading,  and  to  control  its  return  to  battery. 

Kings  Carriage. 

The  chassis  is  steeply  inclined  to  the  rear,  and  the  coun- 
terpoise, which  is  in  a  well,  is  lifted  by  a  rope  passing 
through  the  pintle. 

This  carriage,  invented  by  Major  King  of  the  Engineers, 
is  cheaper  than  the  Moncrieff",  and  has  been  successfully 
tried  in  the  United  States. 

In  both  carriages  exposure  may  be  minimized  by  aiming 
with  mirrors,  and  by  firing  by  an  electrical  contact  automat- 
ically made  when  the  piece  comes  into  battery. 

• 
Regulation  of  Stress. 

1.    BY   FLUID    PRESSURE. 

The  method  now  generally  adopted  is  the  use  of  hydraulic 
or  pneumatic  buffers. 


14  XXII. — ARTILLERY   CARRIAGES. 

These  consist  essentially  of  a  cylinder  and  a  piston,  rela- 
tive motion  between  which  results  from  the  recoil.  The 
effect  is  to  force  the  fluid  contained  in  the  cylinder  through 
orifices  or  ports  which  may  be  either  constant  or  variable 
in  size 

In  the  pneumatic  buffer  the  ports  are  in  the  cylinder  heads ; 
in  the  hydraulic  buffer,  as  the  liquid  is  to  be  used  again,  they 
are  in  the  piston. 

Pneumatic  Buffer, 

This,  although  simpler  and  requiring  less  attention  than 
the  hydraulic  buffer,  is  more  bulky,  can  be  less  easily  regu- 
lated, and  gives  an  injurious  counter  recoil. 

Hydraulic  Buffer, 

Description.  Let  the  arrangement  be  in  principle  such 
as  shown  in  figure  4.  C  is  the  cyUnder  filled  with  a  non- 
freezing  mixture  of  glycerine  and  water ;  it  is  attached  to  the 
carriage  P  is  the  piston  fixed  on  the  rod  R^  which  is  secured 
to  the  chassis. 

Many  alternative  arrangements  are  made. 

By  placing  it  under  tensile  stress  during  the  recoil,  the 
bending  of  the  rod  may  be  avoided. 

The  size  of  the  ports  in  the  piston  may  be  varied  by  the 
profile  of  the  ribs,  r,  which  are  fixed  to  the  interior  of  the 
cylinder,  or  by  a  notched  disc  revolving  on  the  piston  and 
provided  with  projections  which  enter  rifle  grooves  in  the 
cyhnder. 

We  will  consider  only  the  second  period  of  recoil,  and  will 
neglect  the  friction  of  the  liquid  and  that  of  the  rod  in  its 
stuffing  box,  so  that  the  pressure  considered  "^ill  be  that 
required  to  give  a  constant  acceleration  to  the  fluid. 

The  value  of  this  method  appears  from  the  fact  that  it  may 
safely  restrict  the  most  powerful  cannon  to  a  recoil  of  about 
3  calibers. 

\ 


XXn. — ARTILLERY   CARRIAGES.  15 


Notation,  , 

Let: 

A  be  the  area  of  cross-section  of  the  bore  of  the  cylinder 
diminished  by  that  of  the  piston  rod  and  ribs. 

a^  the  total  initial  area  of  the  ports. 

a  this  area  at  the  end  of  the  time,  /,  or  after  a  displace- 
ment, X. 

v'  the  corresponding  velocity  of  the  liquid  current. 

11  the  corresponding  velocity  of  recoil. 

Vq  the  initial  velocity  of  recoil,  obtained  either  by  meas- 
urement or  by  means  of  the  formula 


("'+?) 


.„-       ^_       r;[cos(e,  +  /3)-/sin(9,  +  /3)]        (11) 

derived  from  Equation  (9),  Chapter  VII,  and  the  remarks 
noted  on  pages  7  and  10  herein. 

6  the  density  of  Uquid,  or  the  ttiass  of  one  unit  of  its 
volume. 

P  the  pressure  on  the  piston  at  any  moment. 

a  the  corresponding  acceleration. 

Extent  of  recoil.  If  the  cylinder  is  full,  the  volume  a  v', 
of  liquid  which  in  a  unit  of  time  passes  from  in  front  of  the 
piston  to  the  rear  must  be  equal  to  the  volume,  A  u  caused 
by  the  translation  of  the  cylinder,  whence 


Au 

(12) 

The 

mass  of  the 

liquid 

escaping  in 

the 

time 

A/ 

is  then 

;;/  = 

8av' 

A/=  6  A  u 

A/ 

(13) 

and  its 

energy 

mv"' 

6  A'  u'/\  t 

- 

a4) 

2 

-        2d' 

16  XXII. — ARTILLERY    CARRIAGES. 


This  is  equal  to  the  work  done  by  P  over  the  path  u  A  /, 
and  therefore 

„       d  A"  u^ 

Since  P  is  constant,  Equation  (15)  must  be  true,  for  the 
initial  values  of  u  and  a,  and  therefore 

From  this,  by  equating  the  initial  energy  of  the  system, 
with  the  work  of  the  resistances,  including  the  lifting  of  the 
weight  of  the  system,  and  the  work  of  friction  over  the  path 
iS",  we  have 

~\^^^\_~2^'  +^-^s(sin/3+/cos/?)J,      (17) 

from  which  S  can  be  determined  when  A  and  a^  are  known, 
or  from  which  a^  can  be  determined  when  *S  and  A  are 
known. 

Profile  oj  the  ribs.     From  the  theory  of  energy  we  have 

or 

u=K^l-^-^  (19) 

Also,  since  the  recoil  is  uniformly  retarded  if  we  consider 
the  resistance  of  the  liquid  only,  we  have 

Fl  =  2a  S 
which  value  of  VI  in  Equation  (19)  gives 


«=K\/i-i- 


which  from  Equations  (15.16)  may  be  written 


-V^ 


(20) 


(21) 


XXII. — ARTILLERY   CARRIAGES.  17 


a 
If  there  are  n  similar  ports,  the  area  of  each  one  is  -  -.    If 

n 

each  notch  in  the  piston  has  a  breadth,  b^  and  a  depth,  d^ 

and  the  rib  has  the  same  breadth  and,  as  shown  by  figure  4, 

a  variable  depth,  j,  then 

a  =  nb  {d  —  y)  (22) 

Which  value  of  a  substituted  in  Equation  (21)  and  solved 
with  respect  to  y  gives 

This  is  the  equation  of  a  parabola. 

At  the  end  of  the  recoil,  when  x  =  S,  y  =z  d,  or  the  ports 
are  completely  closed 

This  formula  applies  only  to  the  path  of  the  recoil  after 
the  system  has  acquired  its  maximum  velocity  or  during  the 
second  period. 

While  the  projectile  is  in  the  gun  the  piece  recoils  from  one 
to  two  inches  and  continues  to  gain  velocity  for  four  to  six 
inches  more  so  that  the  maximum  velocity  is  not  attained 
until  after  a  recoil  of  five  to  eight  inches 

Figure  11  shows  these  phenomena  and  the  effects  of  a 
suitable  control,  based  largely  upon  the  analysis  of  velocity 
curves  obtained  during  the  practically  free  recoil  of  the  ])iece. 
The  data  were  as  follows :  Weight  of  piece,  about  100000 
lbs. ;  of  projectile,  754  lbs. ;  of  powder,  244  lbs. ;  initial 
velocity,  1857  f.  s. 

Cylinder,  The  thickness  of  the  walls  of  the  cylinder  may 
be  determined  from  Equation  (4),  Chapter  XIX,  by  placing 


The  area  A  will  be  determined  practically  by  the  construc- 
tion of  the  chassis.     As  the  depth  of  the  chassis  limits  the 


18  XXII. — ARTILLERY   CARRIAGES. 

diameter,  it  is  customary  to  have  two  cylinders  connected  by 
a  tube  so  as  to  equalize  the  resistances  and  prevent  slueing. 

Counter  RecoiL  Owing  to  the  incompressibility  of  most 
liquids  the  tendency  to  counter  recoil  is  slight ;  and,  as  the 
velocity  of  return  is  small,  the  weight  of  the  system  generally 
suffices  to  return  it  to  battery. 

Or  the  hquid  may  be  forced  into  another  vessel  or  a  set  of 
stationary  vessels  containing  air  or  powerful  springs,  which 
store  up  energy  to  return  the  piece  to  battery  when  a  valve 
or  latch  is  opened.  Figure  5  illustrates  the  operation  of  such 
a  carriage.  When  air  is  compressed  by  the  liquid,  the  variety 
is  known  as  the  hydro-pneumatic 

Regulation  of  Stress. 

2      BY   THE    ELASTICITY    OF    SOLIDS. 

The  weight  of  the  cylinder,  and  the  difficulty  of  prevent- 
ing leaks  in  the  preceding  apparatus,  renders  it  objectionable 
in  wheeled  carriages,  and  more  so  for  those  used  in  the  field 
service  than  for  those  in  the  siege  service 

A  compromise  has  therefore  been  sought  by  the  inter- 
position of  an  elastic  solid,  the  work  done  upon  which  in  the 
first  period  will  reduce  the  shock  felt  by  the  system.  The 
restoration  of  this  work  is  not  essential,  although  it  tends  to 
distribute  the  stresses  over  the  path. 

Such  an  arrangement  is  shown  in  the  Engelhardt  (Russian) 
carriage,  figure  6. 

Engelhardt  Buffer.  The  flasks  are  notched  so  as  to  allow 
the  axle,  a^  a  limited  play.  They  are  also  similarly  pierced 
for  the  cross-bar,  ^,  each  end  of  which  is  united  to  the  outer 
end  of  «,  by  a  brace,  k.  This  keeps  the  axle  from  bending 
easily  since  the  force  of  recoil  is  applied  close  to  the  wheels. 

The  transom,  c^  separates  e  from  an  elastic  buffer,  K  The 
buffer  consists  of  layers  of  cork,   rubber,   or  of  Belleville 


XXII. — ARTILLERY   CARRIAGES.  19 


Springs  {post ),  assembled  on  a  bolt,  /,  the  front  end  of  which 
is  secured  to  e,  and  the  rear  end  of  which  is  provided  with  a 
nut,  d. 

When  discharged,  the  piece,  with  its  flasks  and  c  and  b, 
slides  back  relatively  to  the  wheels  and  /  and  ^,  so  that  b  is 
compressed.  A  considerable  proportion  of  the  energy  of  re- 
coil is  thus  absorbed  before  the  wheels  begin  sensibly  to  move. 

After  recoil,  the  elasticity  of  b  restores  the  parts. 

Belleville  Springs,  These  are  saucer  shaped  discs  of  sheet 
steel,  pierced  by  an  axial  hole  by  which  they  are  united  in 
pairs  on  a  spindle,  base  to  base.  They  are  now  much  used 
under  compression  where  space  is  limited. 

Lejnoine  Brake.  The  French  artillery  have  borrowed  from 
the  omnibus  of  Paris  a  more  perfect  but  more  complex  brake, 
figure  12.  On  the  march  it  may  be  set  against  the  tire,  by 
hand,  as  in  the  wagons  of  commerce.  When  the  piece  is 
fired,  the  relative  motion  of  a  mass,  w,  throws  forward  the 
elastic  cross-bar,  b^  to  each  end  of  which  is  attached  a  taper- 
ing cord,  c.  Each  cord  after  making  several  loose  turns 
around  the  nave  is  secured  to  the  brake  beam,  B.  When  m 
is  thrown  forward  it  is  held  in  place  by  the  serrated  edge  of 
an  axial  bar,  b',  to  which  it  is  secured.  The  motion  of  b 
stretches  the  cords  and  tightens  them  around  the  naves  so 
that  they  are  further  wound  up  by  the  revolution  of  the 
wheel  in  recoiling. 

The  greater  the  extent  of  the  recoil  at  any  instant,  and 
therefore  the  less  the  velocity  of  recoil,  the  thicker  will  be 
the  cord  and  therefore  the  greater  will  be  the  increment  of 
the  pressure  of  the  brake  upon  the  tire. 

See  also  the  U.  S.  Buffington  brake  in  the  next  chapter. 

PLATFORMS. 

To  insure  continued  accuracy  of  fire  from  the  same  site, 
it  is  absolutely  necessary  that  the  carriage  should  rest  upon 
a  solid  and  substantial  platform, 


20  XXII. ARTILLERY   CARRIAGES. 

The  mobility  of  field  pieces  restricts  this  necessity  to  the 
sea  coast  and  siege  services. 

In  the  sea  coast  service  the  platforms  are  constructed  by 
the  Engineer  Department  with  the  works  which  the  cannon 
defend. 

Wooden  platforms  are  employed  for  siege  pieces,  in  which 
long  continued  firing  at  one  object  as  in  breaching,  would 
cut  into  the  unprotected  soil  deep  ruts,  which  would  increase 
the  difficulty  of  serving  the  piece  and  restrict  both  its 
horizontal  and  vertical  field  of  fire. 

The  construction  of  the  platform  should  be  such  that  it 
may  be  taken  up  without  injury  for  removal  to  another  site. 

Siege  platforms  consist  of  a  certain  number  of  pieces  of 
wood ;  and  in  order  that  these  pieces  may  be  carried  on  the 
backs  of  soldiers  from  the  depot  to  the  battery,  the  weight 
of  the  heaviest  piece  should  not  exceed  fifty  pounds.  Siege- 
platforms  consist  of  sleepers  (i),  (fig.  7),  and  deck  platik  (2). 
The  general  direction  of  the  sleepers  is  parallel  to  the  axis 
of  the  piece,  and  the  deck-plank  at  right  angles  to  it ;  this 
disposition  of  the  parts  offers  the  greatest  resistance  to  the 
recoil  of  the  carriage.  The  deck-planks  are  fastened  together 
at  their  edges  by  dowels ;  the  outer  planks  are  secured  by 
iron  eye-pins,  one  at  each  end  of  a  sleeper.  The  platform  is 
secured  in  its  place  by  driving  stakes  around  the  edges. 

There  are  two  principal  platforms  for  the  siege-service,  viz., 
the  ^2^;z-platform  and  the  mortar-'^XdXioxm.  The  former  is 
composed  of  twelve  sleepers  and  thirty-six  deck-planks;  the 
mortar-platform  of  six  sleepers  and  eighteen  deck-planks. 

A  simple  and  strong  mortar-platform,  called  the  rail- 
platform  may  be  used  where  trees  or  timber  can  be  easily 
procured.  This  is  composed  of  three  sleepers  and  two  rails, 
secured  by  driving  stakes  at  the  angles  and  at  the  rear  ends 
of  the  rails.  The  rails  are  placed  at  the  proper  distance 
apart  to  support  the  cheeks  of  the  bed. 


XXII. — ARTILLERY    CARRIAGES.  21 

II.  TRANSPORTATION. 

For  certain  light  pieces,  as  machine  guns,  a  two-wheeled 
vehicle  is  used.  Where  the  weight  of  the  load  requires  its 
distribution  on  several  supports,  the  gun  carriage  is  converted 
into  a  four-wheeled  carriage  by  attaching  it  to  another  two- 
wheeled  carriage,  called  the  limber. 

PRINCIPLES    OF    THE    WHEEL. 

In  transportation  the  wheel  is  intended  to  transfer  sliding 
friction  from  between  the  surfaces  of  the  tire  and  the  ground, 
where  the  coefficient  of  friction  is  large  and  variable,  to  the 
lubricated  surfaces  of  an  axle  and  its  bearing,  where  the 
coefficient  is  small  and  nearly  constant. 

In  this  respect  its  value  as  a  mechanical  power  varies 
directly  with  the  radius  of  the  wheel  and  inversely  with  that 
of  the  bearing. 

The  wheel,  as  shown  by  figure  8,  increases  also  the  lever 
arm,  /,  of  the  power,  P,  with  respect  to  that,  q,  of  the  weight, 
W^  to  be  raised  over  the  obstacle,  h. 

On  these  accounts,  since  the  diameter  of  the  bearing, 
which  is  generally  equal  to  that  of  the  axle  arm,  is  fixed  by 
the  maximum  stress  which  the  axle  arm  has  to  support,  the 
mechanical  advantage  of  the  wheel  increases  with  its  diameter. 

An  increase  in  diameter  as  well  as  in  the  width  of  the  tire, 
diminishes  the  pressure  per  unit  of  area  between  the  tire  and 
the  ground,  and  therefore  diminishes  the  rolling  friction,  or 
the  work  lost  in  permanently  deforming  the  ground  on  which 
it  travels.  The  elasticity  of  the  wheel  also  favors  this  reduc- 
tion ;  hence  the  use  for  railways  of  iron  wheels  on  iron 
tracks. 

The  increase  in  size  is  limited  by  the  weight  of  the  wheel, 
the  stability  of  the  system  on  the  march  and  in  firing,  and  the 
convenience  of  loading.  The  mobility  of  transportation 
also  limits  the  size,  for  all  wheels  in  the  same  service  being 


22  XXII. — ARTILLERY   CARRIAGES. 


interchangeable,  the  facility  of  turning  depends  upon  their 
diameter,  as  will  be  shown. 

As  shown  by  figure  8,  an  advantage  also  follows  from 
inclining  the  direction  of  the  draught,  particularly  for  the 
front  wheels,  which  do  most  of  the  work  of  rolling  friction 
and  which  therefore  are  designed  to  carry  only  about  J  of 
the  total  load.  Since  the  point  at  which  the  horse  exerts  his 
power  is  fixed  by  his  conformation,  it  is  evident  that  this 
advantage  will  be  diminished  with  the  increase  of  diameter  of 
the  wheel. 

These  considerations  have  generally  fixed  the  diameter  of 
all  field  artillery  wheels  at  about  5  feet,  and  their  weight  at 
about  200  pounds. 

Siege  wheels  are  made  heavier  and  larger. 


CONSTRUCTION    OF   THE   WHEEL, 

The  requisites  of  size,  weight,  elasticity  and  facility  o.  re- 
pair demand  a  more  general  use  of  wood  in  the  wheel  than  in 
other  parts  of  the  carriage,  and  involve  a  marked  application 
of  the  principle  of  independence  of  function.  This  will  ap- 
pear by  comparing  the  rudimentary  wheel,  still  used  in  remote 
districts,  consisting  of  a  disc  cut  from  the  trunk  of  a  tree,  with 
the  complex  elastic  structure  employed  in  the  bicycle. 

The  Archibald  wheel,  figure  9,  now  much  used  in  the  U.  S., 
resembles  that  now  generally  employed  in  other  services, 
although  it  applies  less  fully  the  principle  above  named. 

Starting  from  the  center,  which  is  the  best  way  of  consid- 
ering any  circular  structure,  we  find  : —  N^  N\  the  7iave  or 
hub.  This  receives  the  pressure  of  the  axle  arm  on  a  lubricated 
surface,  and  distributes  the  pressure  to  the  spokes.  The  nave 
is  made  in  two  parts,  to  facilitate  repairing  the  spokes.  The 
portion  of  the  nave  in  contact  with  the  axle,  or  the  axle  box, 
is  so  shaped  as  to  receive  the  lubricant  in  the  cavity,  O, 


XXII. ARTILLERY    CARRIAGES.  23 

In  some  foreign  wheels  and  in  the  ordinary  wooden  wheel 
the  axle  box  consists  of  a  separate  piece,  so  that  it  may  be 
replaced  when  worn.  Since  friction  is  less  between  dissimilar 
metals  than  between  surfaces  of  the  same  metal,  and  in  order 
to  cause  the  wear  to  take  place  most  on  the  part  which  can 
be  most  easily  replaced,*  the  axle  box,  when  separate,  is  pref- 
erably made  of  phosphor-bronze,  while  the  nave,  as  in  the 
Archibald  wheel,  may  be  made  of  malleable  cast  iron.  The 
metal  nave  marks  a  great  improvement  over  the  wooden  nave 
formerly  employed.  The  cross  section  of  this  piece  made  it 
difficult  to  season,  its  softness  caused  it  to  wear  from  the 
alternate  compression  of  the  vertical  and  extension  of  the 
horizontal  spokes,  and  it  was  especially  exposed  to  decay 
from  moisture  lodging  in  the  angles  between  the  spokes. 

6",  6",  are  the  spokes,  which  transmit  the  weight  to  the  rim. 
For  elasticity  and  facility  of  repair  they  are  made  of  oak  or 
hickory.  Their  inner  extremities  are  shaped  like  voussoirs, 
which  abut  closely  upon  the  box  to  avoid  destructive  play. 
In  the  Archibald  wheel  the  voussoirs  are  made  a  trifle  large 
and  simultaneously  set  together  by  a  powerful  radial  press 
which  subjects  them  to  a  stress  many  times  greater  than  they 
are  likely  to  receive  in  service. 

R  is  the  rmi  which  distributes  the  weight  over  the  ground. 
For  the  same  reasons  as  the  spokes,  and  because  mud  adheres 
less  to  wood  than  to  iron,  the  rim  is  made  of  oak.  In  order 
to  avoid  cutting  too  much  across  the  grain  the  rim  consists 
of  a  number  of  segments  called  felloes  or  fellies. 

T  is  the  tire,  shrunk  on  to  bind  the  parts  together  and  to 
protect  the  rim  from  wear.  As  it  may  require  shortening  in 
order  to  produce  the  necessary  compression  on  parts  which 
have  become  loose  from  wear,  it  is  usually  made  of  wrought 
iron  or  of  low  steel. 

*This  is  an  important  principle  in  machine  design. 


24  XXII. — ARTILLKRY    CARRIAGES. 


The  figure    shows  also    various  bolts    and  clips  and  the 
line h  pin  and  ivasher,  the  functions  of  which  are  evident. 


Dish. 

The  spokes  are  so  arranged  as  to  form  a  conical  surface 
which  is  called  ih^dish.  The  principal  object  of  the  dish  is 
to  give  stiffness  to  the  wheel,  since  (figure  13)  on  a  trans- 
verse slope  or  on  uneven  ground,  the  lower  wheel,  which 
bears  the  greatest  share  of  the  weight,  will  resist  the  lateral 
thrust  of  the  axle  by  a  compressive  stress  upon  the  spoke. 
If  the  spokes  lay  in  the  plane  of  the  rim,  there  would  be  an 
alternating  transverse  stress  on  the  ends  of  the  spokes ;  this 
stress  would  make  them  work  loose  in  their  sockets  and  accel- 
erate the  destruction  of  the  entire  machine. 

Axle. 

T\ie  axle  or  axle  tree  consists  of  the  body  and  the  arms. 
The  arms  are  conical  so  as  to  give  the  greatest  strength  with 
the  least  mean  diameter.  In  some  vehicles,  the  wear  between 
the  arm  and  box  is  taken  up  by  means  of  washers  of  varying 
thickness. 

The  axis  of  the  arm  is  inclined  slightly  downward,  forming 
the  hollow^  and  to  the  front,  forming  the  lead.  Both  together 
constitute  the  set  of  the  arm. 

In  a  dished  wheel  the  hollow  frees  from  transverse  stress 
the  *'  working  spoke,"  which  is  that  which  bears  the  greatest 
load ;  it  also  relieves  the  linch  pin  from  thrust.  For  a  given 
width  of  carriage  body  it  allows  the  axle  body  to  be  made 
shorter  and  therefore  stronger ;  and,  from  the  inclination  of 
the  plane  of  the  rim,  it  tends  to  throw  the  mud  clear  of  the 
carriage. 

The  efiect  of  the  lead  is  to  diminish  the  transverse  stress 
upon  the  front  spoke  in  meeting  obstacles. 


XXII. — ARTILLERY   CARRIAGES.  25 

Axle  Body. 
Although  the  interval  between  the  cheeks  transfers  the 
transverse  stress  upon  the  axle  to  points  near  the  wheels,  it 
was  found  necessary  in  former  carriages  to  reinforce  the  axe 
with  a  wooden  body.  In  modern  carriages  this  is  sometimes' 
replaced  with  two  grooved  plates  which  clamp  the  cylindrical 
axle  between  them  and  are  extended  to  the  front  and  rear  so 
as  to  stiffen  the  axle  in  recoihng.  They  also  serve  to  fasten 
the  axle  to  the  cheeks.  The  axle  may,  without  sensible  loss 
of  strength,  be  made  hollow,  and  three-fourths  of  its  weight 
when  solid. 

THE    STOCK. 

The  prolongation  of  the  cheeks  is  called  the  stock.  The 
use  of  metal  instead  of  wood,  has  permitted  a  return  to  the 
construction  of  the  great  French  designer.  General  Gribeau- 
valy  in  whose  gun  carriages  the  flasks  were  parallel  extensions 
of  the  cheeks. 

The  metallic  flasks  now  used  converge  to  the  trail. 

In  the  stock  trail  syste?n,  recently  in  use,  the  cheeks  con- 
tained between  them  a  single  piece  of  wood  called  the  stock. 

Besides  its  functions  under  fire  the  stock  of  the  gun  carriage 
unites  the  two  axles  of  the  four-wheeled  vehicle,  as  does  the 
reach  or  perch  of  the  ordinary  vehicle.  For  artillery  carriages 
used  simply  for  transportation,  such  as  the  caisson  and  the 
forge,  the  stock  is  a  single  piece  of  wood  joining  the  body  to 
the  limber. 

Tiirnmg  A?igle. 

The  dimensions  of  the  stock  affect  the  mobility  in  turning. 
This  is  often  measured  by  the  tiirfiing  angle,  which  is  half  the 
horizontal  angle  through  which  the  pole  can  revolve  when 
the  carriage  is  at  rest.  Practically,  the  space  required  to  turn 
the  carriage  will  vary  with : 

1.  The  length  and  width  of  the  line  of  horses  and  their 
gait. 


26  XXII. — ARTILLERY    CARRIAGES. 

2.  The  distance  of  the  pintle  from  the  vertical  plane  tan- 

gent to  the  rear  face  of  the  front  wheels. 

3,  The  thickness  of  the  stock  at  the  point  rubbed  b"  the 

wheels  in  turning. 
•    4.  The  length  of  the  stock. 

Owing  to  the  first  condition  above  named  a  turning  angle 
of  60°  is  generally  considered  as  sufficient.  This  may  be 
increased  by  increasing  the  distance  of  the  pintle  from  the 
front  axle,  but  this  is  apt  to  cause  the  pole  to  *'  thrash." 

Pintle. 

The  distance  of  the  pintle  in  rear  of  the  axle  in  connection 
with  the  moment  of  the  trail,  afiects  also  the  pressure  on  the 
necks  of  the  wheel  horses  caused  by  the  moment  of  the  pole. 

In  siege  carriages  and  in  those  used  only  for  draught,  the 
pintle  is  placed  at  some  distance  to  the  rear ;  or  a  similarly 
placed  transverse  sweep  bar  is  used,  which  supports  the 
weight  of  the  stock. 

But,  in  field  carriages  for  which  flexibility  of  attachment 
and  mobility  are  essential,  the  pintle  is  placed  more  to  the 
front  and  the  evil  corrected  as  far  as  possible  by  distributing 
the  load  or  by  various  mechanical  means. 

In  this  arrangement  the  preponderance  of  the  system  com- 
posed of  the  gun  and  its  carriage  is  an  important  factor.  If 
the  trunnion  beds  are  moved  towards  the  Hmber  the  pole  is 
lifted,  but  the  labor  of  Hmbering  is  increased,  and  the  sta- 
bility of  the  carriage  in  firing  is  diminished.     (Eq.  9.) 

To  diminish  the  labor  of  limbering,  the  pintle  is  placed  as 
low  as  permitted  by  the  requirement  that  as  much  free  space 
as  possible  should  be  left  beneath  the  axles  for  mobility  on 
ground  covered  with  large  stones,  stumps,  etc. 

In  the  siege  service,  as  the  piece  does  not  require  to  be 
brought  into  action  rapidly,  and  as  the  limber  carries  no 
extra  load,  the  piece  may  be  shifted  to  the  traveling  trunnion 


XXII. — ARTILLERY    CARRIAGES.  27 

beds  which,  on  the  march,  are  in  front  of  those  from  which 
the  piece  is  fired. 

THE    LIMBER. 

Nomenclature. 

The  wooden  field  Umber,  figure  10,  is  composed  of  an 
axle  tree  (1) ;  a  fork  (2) ;  two  hounds  (3,  3) ;  a  splinter  bar 
(4) ;  two  foot  boards  (5,  5) ;  a  pole  (6)  ;  the  pintle  hook  and 
key  (7);  two  pole  yokes  (8,  8);  and  pole  pad  {^). 

Ahhough  destined  to  be  soon  replaced  by  one  composed 
more  largely  of  steel,  it  is  here  discussed  as  it  illustrates  some 
valuable  principles- 

The  hounds  serve  to  support  the  ends  of  the  limber  chest 
and  the  foot  boards,  and  also  to  transmit  the  draught  of  the 
horses  from  the  splinter  bar  to  the  axle. 

The  pole  or  totigue  is  employed  to  stop  the  carriage  and  to 
give  it  direction.  As  it  is  liable  to  be  broken,  it  is  practically 
made  in  two  pieces,  of  which  the  fork,  which  is  least  exposed 
to  accident,  forms  one.  The  fork  then  is  a  socket  for  the 
pole,  and  braces  the  entire  frame  by  its  attachment  to  the 
axle  body  and  the  parts  in  front. 

The  pole  should  be  so  attached  to  the  fork  that  it  may  be 
readily  replaced  when  broken. 

The  pole  yokes  transfer  the  weight  of  the  free  end  of  the 
pole  to  the  necks  of  the  wheel  horses  and  the  soft  pad  pro- 
tects the  leading  horses  from  harm. 

Attachments, 

The  metaUic  limber  body  consists  of  channel  irons  and  T 
angle  irons  united  in  various  ingenious  ways.  The  rigid 
splinter  bar  may  be  replaced  by  the  ordinary  jointed  double 
tree  and  si?tgle  trees.  These  permit  the  horses  to  work  more 
independently  of  each  other  than  the  splinter  bar  does,  but 
are  probably  not  so  strong.  A  joint  is  always  a  cause  of 
expense  and  generally  a  source  of  weakness. 


28  XXII. — ARTILLERY    CARRIAGES. 

In  the  British  service  the  pole  is  replaced  by  shafts. 
Since  the  pace  of  the  team  is  regulated  by  that  of  the  slowest 
horse,  this  arrangement,  while  more  manageable  than  the 
pole,  and  therefore  better  fitted  for  the  showy  evolutions  of  a 
drill,  is  objectionable  for  the  march,  since  the  work  which 
devolves  on  the  shaft  horse  diminishes  his  endurance. 

The  Limber  Chest 

This  serves  to  carry  ammunition,  and  also  furnishes  a  seat 
for  some  of  the  cannoneers.  The  gun  carriage  is  often 
arranged  to  carry  two  cannoneers  on  side  seats,  in  order  to 
diminish  the  time  required  for  coming  into  action,  a  matter 
which,  owing  to  the  precision,  rapidity  and  range  of  infantry 
fire,  is  becoming  of  vital  importance.  The  carriage  also 
often  carries  two  rounds  of  canister  for  use  at  close  quarters. 

The  principal  distinction  between  limber  chests  depends 
upon  how  the  lids  are  placed. 

If  on  top,  the  chest  may  easily  be  made  waterproof  in 
fording  streams ;  but  the  contents  are  less  accessible.  If 
behind,  the  lid  may  form  a  convenient  tray  for  preparing 
fuzes,  &c.  This  arrangement  is  more  liable  to  accidental 
opening  than  the  former,  and  waterproof  packages  for  the 
cartridges  may  be  necessary. 

The  ammunition  chests  in  the  U.  S.  Service  are  still  con- 
structed of  wood.  In  other  countries  sheet  steel  is  generally 
used.  For  what  reason  is  unknown  ;  since,  if  not  unduly 
heavy,  they  are  not  proof  against  infantry  fire. 

THE    MORTAR   WAGON. 

This  is  used  for  transporting  siege  projectiles,  mortars  and 
their  beds,  and  spare  guns. 

The  body  consists  of  a  strong,  rectangular  frame  provided 
with  a  stock  by  which  it  is  attached  to  the  siege  limber.  At 
the  rear  of  the  body  is  placed  a  windlass  which  aids  in  loading 


XXII. ^ARTILLERY    CARRIAGES.  29 

heavy  weights.  Stakes  may  be  placed  around  the  sides  to 
sustain  boards  used  in  retaining  loose  objects. 

Since  rifle  projectiles  are  always  issued  boxed  instead  of 
loose,  as  was  the  former  custom,  the  necessity  of  the  mortar 
wagon  for  their  transportation  no  longer  exists;  but  its 
general  utility  is  great.  It  will  .probably  be  used  hereafter 
for  transporting  siege  guns  for  considerable  distances,  since 
the  height  of  the  carriage  from  which  they  are  now  fired 
renders  them  unstable  on  rough  roads. 

A  special  wagon  with  a  crank  axle,  so  arranged  as  to  carry 
the  load  close  to  the  ground  without  diminishing  the  height 
of  the  wheels  would  appear  to  offer  special  advantages. 

III.  CARRIAGES  FOR  SUPPLY. 

New  U.  S.  System. 

These  include,  1st,  the  caisson^  for  carrying  a  larger  quan- 
tity of  ammunition  than  can  be  carried  by  the  limber,  and 
also  a  spare  pole,  wheel,  handspikes,  buckets  and  tools ; 
2nd,  the  forge  and  battery  wagon,  containing  a  larger  assort- 
ment of  tools  and  material  for  repairs ;  3rd,  the  artillery 
store  wagon,  an  ordinary  four-horse  wagon,  containing  extra 
small  arms  and  ammunition  and  the  men's  knapsacks,  etc., 
so  as  to  confine  the  load  of  the  fighting  teams  to  the  neces- 
sities of  action. 

REMARK. 

The  increased  weight  of  each  round  of  modern  ammuni- 
tion and  the  necessity  for  an  even  greater  number  of  rounds 
than  formerly  sufficed,  increases  the  difficulty  of  supply. 

It  is  proposed  abroad  to  increase  the  number  of  caissons 
per  piece  and  to  retain  the  supply  in  the  limber  for  extreme 
emergencies. 


XXtil.  — VARIOUS  AkTiLLEkY  CaRria6E§. 


CHAPTER  XXIII. 
VARIOUS  ARTILLERY  CARRIAGES. 

The  U.  S.  Field  Carriage.    Figures  1-4. 

Constmction, 

This  carriage,  designed  by  Colonel  Buffington  of  the  Ord- 
nance Department,  is  made  of  steel,  since,  owing  to  the  large 
value  Qii  h  of  this  gun  (Chapter  XI,  page  21),  wooden  car- 
riages, and  even  some  differently  constructed  of  steel,  were 
found  insufficiently  strong. 

The  principal  features  relate  to  the  construction  of  the  axle 
body,  of  the  stock  and  to  the  operation  of  the  brake.  The 
hollow  cylindrical  axle  is  strengthened  by  axle  plates,  figure 
2,  which  stiffen  it  in  the  direction  of  the  recoil.  The  stock 
consists  of  two  brackets,  each  of  which  is  made  of  two  nearly 
symmetrical  sheets  of  steel  stamped  hot  between  dies  so  as  to 
give  the  corrugated  cross  section  indicated  in  figure  3.  When 
riveted  through  the  webs,  each  bracket  forms  a  strong,  light 
truss,  resisting  stress  both  in  its  own  plane  and  transversely. 

The  lower  flanges  of  the  outer  plates  project  inwardly  and 
serve  to  unite  the  brackets  to  the  axle  plates.  The  brackets 
are  further  united  by  transoms,  three  of  which  with  a  hinged 
lid  form  the  trail  box  for  the  oil  can  and  tools  which  have 
become  a  necessary  portion  of  the  equipment. 

The  carriage  is  provided  with  two  axle  seats  for  cannoneers. 

The  wooden  handspike  is  permanently  hinged  to  the  trail. 

Elevating  Screw, 

The  space  between  the  brackets  allows  the  breech  to 
descend  sufficiently  for  the  high  angles  of  fire  used  with  low 


XXIII. — VARIOUS   ARTILLERY   CARRIAGES. 


charges  against  troops  sheltered,  from  view,  and  the  crank 
which  operates  the  elevating  screw  is  placed  at  the  side,  so 
that  under  these  conditions  it  will  be  readily  accessible. 

The  nut  of  the  elevating  screw  oscillates  slightly  on  trun- 
nions, and  the  head  of  the  screw  is  connected  by  a  fork  to 
an  axis  parallel  to  and  beneath  the  trunnions,  so  that,  as  the 
angle  of  fire  changes,  the  axis  of  the  screw  will  be  nearly 
normal  to  that  of  the  gun. 

Brake. 

The  great  strength  of  this  carriage  has  permitted  the 
employment  of  Colonel  Buffington's  brake,  figure  4. 

This  consists  of  an  [_  shaped  rod,  the  stem  of  which  is 
surrounded  by  a  spiral  spring  contained  within  a  tube  ;  the 
rod  swings  freely  from  a  loose  joint  situated  eccentrically 
above  the  axle. 

The  length  of  the  brake  is  such  that  when  held  vertically 
the  hook  will  pass  over  the  wheel ;  and,  being  allowed  to  fall 
to  the  rear,  it  will  engage  with  the  tire  at  some  point  as  a. 

When  the  wheel  revolves  in  the  recoil,  the  friction  at  a 
tends  to  extend  the  rod.  But  this  compresses  the  spring  and 
increases  friction,  so  that  as  the  velocity  of  recoil  decreases, 
the  resistance  to  rolling  increases,  and  the  retardation 
a])proaches  constancy,  at  least  during  the  critical  period 
preceding  sliding. 

The  recoil  has  thus  been  reduced  from  26  feet  to  8  feet, 
without  injury  to  the  carriage. 

In  transportation  the  brake  is  secured  vertically  to  one  of 
the  seat  arms.     It  may  also  be  used  as  a  traveUng  brake. 

Limber  and  Caisson. 
These  carriages  are  constructed  substantially  on  the  lines 
previously  named.     Steel  angle  irons  are  largely  used  for  the 
frame. 


XXIII. — VARI6US    ARTILLERY   CARRIAGES.  3 

The  chests,  which  are  of  wood,  open  on  top  and  are  only 
high  enough  to  receive  the  projectile  standing ;  this  brings 
the  center  of  gravity  very  low. 

The  cartridges  lie  in  a  compartment  between  the  two  end 
compartments  reserved  for  the  projectiles,  which  thus  serve 
to  protect  the  powder  from  hostile  fire. 

For  safety,  no  friction  primers  are  carried  with  the  powder, 
as  was  formerly  done.  Unbroken  packages  are  placed  in 
outside  cases,  and  loose  primers  are  carried  with  the  tube 
pouch  in  the  trail  box. 

The  four  chests  per  piece  can  carry  42  projectiles  each, 
with  a  greater  number  of  cartridges  for  curved  fire. 

The  Siege  Carriage.    Figure  5. 

The  principal  feature  of  this  carriage  is  its  height.  For 
the  protection  of  the  gunners  the  axis  of  the  trunnions  is 
placed  6  feet  above  the  ground. 

In  order  to  prevent  the  system  from  tipping  forward  in 
limbering,  the  trunnions  are  so  placed  that  when  limbered 
the  center  of  gravity  of  the  system  will  fall  between  the  axles. 

The  wheels,  axle  plates  and  brakes  are  such  as  just 
described. 

The  carriage  is  intended  to  transport  the  piece  only  for 
short  distances  about  the  work  which  it  defends. 

REMARK. 

A  small  hydraulic  buffer  connecting  the  stock  with  a  pintle 
sunk  into  the  platform  between  the  wheels,  and  two  movable 
chocks,  assist  in  controling  the  recoil.  The  chocks  rotate 
around  the  pintle  with  the  gun  and  serve  to  return  the  piece 
into  battery. 

The  Siege  Howitzer  Carriage.    Figure  6. 

The  piece  is  mounted  in  two  trunnion  carriages,  a,  upon 
the  inclined  slides,  '^,  upon  which  it  is  allowed  a  recoil  of  six 


4  XXIII. — VARIOUS    ARTILLERY    CARRIAGES. 

inches.  The  recoil  upon  the  shdes  is  checked  by  the 
hydrauhc  cyUnders,  r,  and  the  courses  of  Belleville  springs, 
d.  The  latter  serve  to  return  the  piece  to  the  firing  position. 
They  rest  against  the  traveling  trunnion  beds,  e^  and  the  rods 
upon  which  they  are  strung  pass  through  holes  in  these  beds. 

The  flasks,  /,  are  of  rolled  steel  plate  \  inch  thick,  and  are 
flanged  inward  except  on  their  upper  edges.  From  each 
flask  is  cut  a  large  triangular  piece  in  order  to  diminish  its 
weight ;  the  edges  of  the  apertures  being  flanged  inward  as 
above.  The  flasks  are  xmited  by  three  transoms,  ^,  and  the 
double  transom,  //,  to  which  is  fastened  the  piston  rod  of  the 
hydraulic  brake. 

The  flasks  rest  upon  the  axle  through  two  iron  forgings,  /, 
and  are  strengthened  by  two  supporting  plates,/. 

In  order  to  facilitate  the  elevation  of  the  piece  a  pecuhar 
arrangement  is  employed.  This  consists  of  the  elevating 
rack,  /,  which  is  attached  to  the  piece,  and  the  worm,  m  ;  the 
shaft,  ;/,  and  the  hand-wheel,  o.  The  worm  is  attached  to 
the  right  trunnion  carriage,  and  in  recoihng  slides  along  the 
shaft,  n.  A  spline  (see  AVebster)  on  the  shaft  permits  the 
worm  to  shde  along  the  shaft,  and  yet  constrains  it  to  follow 
in  any  position  the  rotation  given  to  the  hand-wheel,  o. 

The  advantage  claimed  from  this  design  is  that  the  recoil 
of  the  piece  upon  the  carriage  so  diminishes  the  maximum 
stress  upon  the  flasks  and  trail  that  their  weight  may  be 
greatly  reduced.  A  portion  of  the  weight  so  saved  is  used 
to  strengthen  the  axle  and  the  wheels. 

Weight  of  wheels,  375  pounds,  each. 
Weight  of  carriage,  complete,  3200  pounds. 
Pressure  of  trail  on  platform,  13(K)  pounds. 
Height  of  trunnions,  6  feet. 


XXIII. — VARIOUS    ARTILLERY    CARRIAGES.  5 

Barbette  Sea  Coast  Carriage.* 

The  principal  feature  of  the  gun  carriage  is  borrowed  from 
the  old  *' flank-defense  howitzer"  carriage. 

Its  object  is  to  return  the  piece  to  battery  and  by  diminish- 
ing the  variable  work  of  sliding  friction  to  increase  that  of 
the  hydraulic  buffer,  which  can  be  made  constant. 

Each  cheek  carries  two  rollers ;  that  in  rear  is  on  an 
eccentric  axle  and  that  in  front  is  on  a  concentric  axle. 
When  the  piece  is  in  battery  the  front  rollers  are  nearly  in 
contact  with  the  chassis  rail ;  while  those  in  rear  are  usually 
raised  from  it,  but  may  be  thrown  in  contact  by  means  of  the 
eccentric.  The  lower  front  angles  of  the  cheeks  are  trun- 
cated, so  that,  when  the  carriage  is  thus  tilted  to  the  front,  all 
the  rollers  come  into  play  and  the  piece  may  be  moved  from 
battery  with  comparative  ease. 

In  firing,  the  rear  rollers  are  out  of  gear  so  that  the  vertical 
thrust  of  recoil  is  borne  by  the  lower  face  of  the  cheek  and 
the  axles  are  not  endangered. 

As  the  carriage  recoils  the  rear  rollers  strike  inclined  planes 
bolted  to  the  upper  surface  of  the  chassis  rails  and  tilt  the 
carriage  sufficiently  to  cause  it  to  move  by  rolling  until  it 
returns  again  to  battery. 

Muzzle-loading  guns  are  retained  from  battery  by  means  of 
an  automatic  latch. 

MODERN   TYPES    OF    SEA    COAST   CARRIAGES. 

Owing  to  our  deficiency  in  modern  cannon  the  U.  S.  have 
not  yet  (1891)  decided  on  any  special  pattern  of  sea  coast 
carriage;  but  the  following  examples,  derived  from  the 
French  service,  probably  contain  the  essential  features  of  the 
system  to  be  adopted  for  the  barbette  carriages,  as  soon  as 
the  new  cannon  shall  have  been  supplied. 

*  The  Sea  Coast  Battery  at  West  Point  contains  several  specimens  of 
this  type. 


O  XXIII. — VARIOUS    ARTILLERY    CARRIAGES. 

The  types  of  disappearing  carriages  and  those  designed 
for  turrets  are  too  numerous  for  description  here.  They 
generally  apply  the  principles  previously  discussed  with  those 
treated  in  the  course  of  Military  Engineering. 

Gun  Carriage. 

Figures  7,  8  represent  the  elements  of  a  modern  sea  coast 
barbette  gun  carriage.  It  consists  of  three  main  parts  :  1st, 
the  top  carriage,  T^  consisting  essentially  of  the  buffer;  2nd, 
the  chassis,  C,  the  lower  part  of  which  is  circular ;  by  means  of 
a  great  number  of  loose  conical  rollers,  it  revolves  upon  the 
circular  pintle  platform,  P.  This  platform,  cast  in  a  single 
piece,  rests  upon  a  proper  foundation. 

To  avoid  the  complications  due  to  sliding  friction  during 
recoil,  the  top  carriage  also  moves  on  rollers  recessed  in  the 
chassis  rail. 

Pointing  in  azimuth  is  performed  by  an  endless  chain 
engaging  in  a  sprocket*  bed  around  the  platform.  The  chain 
passes  over  a  windlass,  W,  which  is  rotated  by  the  crank,  K, 

The  loading  scoop,  s,  is  on  a  lever,  L,  which  is  rotated  by 
a  geared  crank  so  as  to  bring  both  the  charge  and  the  pro- 
jectile into  the  position  of  loading. 

In  order  to  minimize  the  number  of  men  required  for 
loading,  the  act  of  lowering  the  scoop  stores  up  energy  in 
certain  springs  so  that  the  maximum  pressure  which  can  be 
counted  on  shall  be  continuously  apphed,  as  in  the  hydraulic 
buffer. 

The  steel  shield,  /,  protects  the  gunners  from  light  pro- 
jectiles. 

Advantages,  The  carriage  is  low,  stable,  and  as  seen  in 
figure  9,  very  compact.  The  use  of  rollers  increases  its 
mobility  and  their  number  distributes  the  thrust  over  a  large 
area.     All  wheels  are  protected  and  the  traversing  chain  is  of 


*  See  Webster. 


XXIII. — VARIOUS    ARTILLERY    CARRIAGES.  7 

rustic  simplicity  and  easy  of  repair,  even  in  action.  The 
arrangement  of  the  scoop  facilitates  loading  since  its  load 
may  be  placed  by  simply  tilting  the  hand  truck  on  which  it 
is  brought  from  the  magazine. 

Sea  Coast  Mortar  Carriages.    Figures  10,  11. 

Although  of  an  entirely  novel  design,  the  carriage  in  figure 
10  resembles  essentially  the  gun  carriage  just  described.  The 
nomenclature  is  the  same  in  both  figures. 

The  chassis  is  divided  into  two  portions,  Ci,  C^ ;  the  sur- 
face of  contact  being  cylindrical  about  the  axis  of  the  trun- 
nions. By  this  arrangement  fon  all  angles  of  fire  the  axis  of 
the  gun  is  always  in  the  plane  of  the  axes  of  the  hydraulic 
cylinders,  so  that  the  friction  in  starting  is  not  increased  by 
the  pressure  causing  recoil. 

Rotation  from  recoil  is  prevented  by  the  clips,  c,  c,  etc. 

The  diminished  intensity  of  the  maximum  vertical  pressure 
has  caused  this  carriage  to  be  adopted  in  the  French  Navy; 
for  ships  now,  as  well  as  forts,  are  beginning  to  utilize  the 
advantages  of  vertical  fire. 

In  another  type  of  mortar  carriage,  shown  in  figure  11,  also 
under  trial  in  the  U.  S.,  the  chassis  is  made  in  one  piece,  the 
direction  of  the  recoil  being  downward  at  a  constant  angle  of 
60°  This  is  a  mean  between  the  limiting  angles  of  6  for 
mortar  fire,  viz. :  45"  and  75°.  The  mortar  is  returned  to 
battery  by  springs  that  are  compressed  during  the  recoil. 

Another  form  of  loading  scoop  is  also  shown. 

This  is  known  as  the  Easton- Anderson  carriage,  of  Eng- 
lish design. 


XXIV. — H0RS£   AND   HARNESS. 


CHAPTER  XXIV. 

HORSE  AND  HARNESS. 

The  horse  transports  his  load  in  two  ways.  1st,  as  a  pack 
horse ;  2nd,  as  a  draught  horse. 

PACK    HORSE. 

The  daily  work  of  a  pack  horse  is  about  equal  to  that  of 
five  men  similarly  employed ;  or,  if  he  moves  at  a  walk,  he 
may  carry  a  load  of  200  pounds  25  miles  a  day,  or  5000  mile- 
pounds. 

If  he  trots,  the  increased  expenditure  of  muscular  energy 
reduces  his  daily  work  about  one-third.* 

In  the  above  the  weight  of  the  horse  is  neglected,  and  it  is 
assumed  that,  though  this  daily  work  may  be  temporarily  ex- 
ceeded, the  excess  cannot  be  long  continued  without  injury. 

The  mule,  owing  to  his  build,  carries  more  than  the  horse ; 
he  eats  less  and  is  surer  of  foot.  He  is  therefore  generally 
used  in  the  mountain  service. 

DRAUGHT    HORSE. 

Load. 

Although  a  horse  can  pull  much  less  than  he  can  carry, 
the  advantages  of  the  wheel  enable  him  to  draw  over  ordinary 
roads  a  load  weighing  about  seven  times  as  much  as  his  pack. 
With  a  pull  of  80  pounds  the  daily  work  of  a  draught  horse 


*  It  has  been  found  that  for  any  animal  the  maximum  rate  of  work  per 
unit  of  time  (or/  z/,  Chapter  XI,  page  4)  is  attained  when  the  velocity  is 
about  I  of  the  maximum  velocity  unloaded,  and  the  load  about  g  of  the 
maximum  load  at  the  lowest  positive  velocity. 


XXIV. — HORSE   AND    HARNESS. 


is  generally  given  as  1600  pounds  X  23  miles,  or  36800  mile- 
pounds  of  load,  or  1840  mile-pounds  of  actual  work. 

Owing  to  their  interference  with  each  other's  motions,  the 
maximum  load  drawn  by  teams  of  horses  increases  less  rapidly 
than  does  the  number  of  horses  in  draught.  Thus,  when  the 
teams  comprise  respectively  2,  4,  6,  8  horses,  the  maximum 
loads  which  they  can  continuously  draw  are  in  the  relation 
per  team,  of  the  numbers  9,  8,  7,  6. 

These  considerations,  the  mobility  of  the  system  (Chapter 
XXII,  page  1),  the  increased  weight  of  forage  and  length  of 
column  required,  have  generally  fixed  the  limit  of  efficiency 
at  the  six-horse  team. 

It  is  estimated  that  when  a  draught  horse  carries  a  rider, 
his  efficiency  is  diminished  J  at  a  walk  and  §  at  a  trot.  Con- 
sequently, supplying  the  data  given,  the  maximum  load  for  a 
team  of  6  horses  moving  at  a  trot  will  be  about 


near  files.  off  files. 

3  X  1600       3  X  1600 
+  ^ 


^1  =  3733  pounds; 


or  622  pounds  per  horse. 

This  may  be  considered  2i  physical  constant^  the  best  method 
of  distributing  which  between  the  objects  transported  and  the 
means  of  transportation  is  still  open  to  inquiry. 

Various  conditions  must  be  allowed  for :  On  one  hand  are 
bad  roads,  insufficient  food,  rapid  movements  for  short  times, 
and  forced  marches.  On  the  other  hand,  the  reduction  in 
the  load  caused  by  the  expenditure  of  ammunition,  the  dis- 
mounting of  the  cannoneers,  and  the  infrequency  of  the  trot. 

Upon  these  considerations  are  based  the  following  approx- 
imate loads  per  horse. 

Horse  artillery,  650  pounds. 

Light  field  artillery,  700  pounds. 

Heavy  field  artillery,  850  pounds. 

Siege  artillery,  1000  pounds. 


XXIV. — HORSE   AND   HARNESS. 


REMARK. 

The  12  pdr.  Napoleon  gun,  which  was  the  heaviest  field 
gun  used  in  our  civil  war,  and  which  traveled  over  roads  quite 
as  bad  as  any  used  in  foreign  wars,  gave  a  load  of  645  pounds 
per  horse,  and  was  found  amply  mobile.  The  load  per  horse 
for  the  3.2  inch  B.  L.  R.,  field,  is  632  pounds. 

Angle  of  Draught. 

The  power  of  an  animal  in  draught  may  be  supposed  to 
consist  in  his  ability  to  maintain  himself  rigidly  in  a  position 
such  that  the  moment  of  his  weight  may  be  increased  without 
increasing  the  lever  arm  of  the  resistance. 

Thus  in  figure  1,  let  /  be  the  position  on  the  ground  line, 
/  g,  of  the  hind  feet  of  the  horse  in  draught.  Let  s  be  the 
shoulder  of  the  horse  or  the  point  at  which  he  applies  his 
power  to  the  trace,  s  c,  which  is  attached  to  the  carriage  at 
the  point  c.  Let  W  be  the  weight  of  the  horse,  and  /  be 
the  distance  from  /  on  the  line  /  s,  of  the  vertical  passing 
through  his  center  of  gravity.  Let  r  be  the  tension  on  the 
trace,  the  length  of  which  s  c  ■=.  t^  and  let  R  be  the  horizontal 
component  of  r,  producing  uniform  motion  of  the  point  c  in 
a  horizontal  plane. 

Let  /  be  the  variable  angle  with  the  ground  line  of  the  line 
s  /,  and  g}  be  the  variable  angle  between  s  f  and  s  c.  Let 
^,  drawn  from  /,  perpendicular  to  s  c,  be  the  lever  arm  of 
the  resistance.  Let  the  same  symbols  **  primed  "  represent  a 
new  position  of  the  system  caused  by  the  horse  bending  his 
knees  in  pulling.  For  simplicity,  we  will  suppose  that  his 
fore  feet  are  otf  the  ground  and  that  his  hind  legs  are  not 
extended  so  as  to  increase  /,  as  these  suppositions  tend  to 
neutralize  each  other.  Also  that  the  center  of  gravity  is  on 
the  line  f  s. 

The  construction  of  the  figure  shows  that,  as  the  point  s 
moves  to  s',  c  will  move  to  c\  and  that  R  will  increase  until 


XXIV. — HORSE   AND    HARNESS. 


the  compression  along  s  f  causes  the  horse  to  bend  so  that  / 
will  shorten. 

The  stress  R  may  under  these  circumstances  be  deduced  as 
follows  : 

From  the  equaHty  of  moments  we  have  W I  cos  i-=.r  h, 

and  from  the  figure 

.         W  I  cos  i  cos  ii  —  (p) 
i?  =  r  cos  (?  —  g))  = ^^ ^ 

Graphical  construction  shows  that,  as  i  diminishes,  h  and 
qp  will  diminish  slowly,  and  /  —  qp  will  rapidly  approach  zero. 

R  will  have  its  maximum  value  when  s  falls  on  the  line  c  p^ 
either  from  raising  the  point  of  attachment  to  the  load  at  c  or 
from  the  descent  of  the  point  of  appHcation  of  the  power  at  s. 
This  value  is  not  realized  in  practice,  since,  in  addition  to  the 
effect  noted  above,  as  i  decreases  the  force  of  friction  at  / 
decreases  and  the  feet  tend  to  slip. 

A  proper  inclination  of  the  trace  is  therefore  valuable  since 
it  enables  R  to  be  increased  according  to  the  ability  and 
willingness  of  the  horse,  and  also  that  it  enables  him  to  draw 
by  increasing  the  friction  between  his  feet  and  the  ground. 

By  experiment  it  was  found  that  when  the  horse  is  free, 
the  maximum  practical  value  of  R^  or  about  0.6  W^  was 
attained  for  a  value  of  i — 9  =  12°.  When  the  horse  had 
a  rider,  i — 9  could  profitably  be  reduced  to  7°.  From 
these  data  it  is  estimated  that,  since  tan  12°=  0.2,  a  draught 
horse  should  carry  \  of  his  load  on  his  back. 

The  preceding  general  considerations  apply  to  the  case  of 
men  pulling  on  ropes  or  pushing  on  capstan  bars,  etc.  They 
partly  explain  also  that,  while  for  the  horse  the  maximum 
value  of  i?=0.6  W^  for  man,  it  is  found  practic  ''"  that 
R^W, 

Arrangement  of  the  Horses. 

Owing  to  the  difficulty  of  coordinating  the  movement  of 
the  horses  the  single  file  is  used  only  when  the  gait  is  slow 


XXIV. — HORSE    AND    HARNESS. 


and  the  road  smooth,  so  that  the  shaft  horse  will  not  be  un- 
duly fatigued  by  frequent  changes  of  direction. 

When  the  double  file  is  used,  the  control  of  the  direction 
is  shared  by  the  horses  of  the  wheel  team,  provided  the  car- 
riage have  a  pole. 

This  team  is  preferably  attached  to  a  movable  double  tree^ 
Chapter  XXI F,  page  28,  since  this  shows  by  its  inclination 
whether  the  horses  are  pulling  evenly,  and  also  transfers  the 
draught  to  the  axis  of  the  carriage.  For  these  reasons  it  is 
often  called  the  evener. 

By  attaching  the  traces  to  the  single  trees  hooked  on  to 
each  end  of  the  double  tree,  greater  flexibiHty  is  attained; 
and,  since  the  shoulders  of  the  horse  are  naturally  brought 
into  bearing  alternately,  he  is  less  apt  to  be  chafed  by  the 
sliding  of  the  collar. 

He  may  also,  when  harnessed,  be  more  readily  hitched 
and  unhitched. 

In  commerce  the  leading  team  is  generally  attached  to 
an  evener  fastened  to  the  front  end  of  the  pole.  This  is 
objectionable  since  it  confuses  the  functions  of  the  pole. 
A  better  method,  sometimes  followed,  is  to  support  the 
evener  by  the  pole,  and  to  connect  it  with  the  axle  by  an 
independent  tensile  member,  as  by  a  chain. 

In  the  present  arrangement,  the  objections  to  supporting 
the  weight  of  the  evener  on  the  end  of  the  pole,  and  here- 
fore  on  the  necks  of  the  wheel  team,  are  avoided,  and  the 
traces  of  each  team  are  connected  with  those  in  rear  by  an 
arrangement  which  permits  continuous  draught  without  caus- 
ing the  effort  of  wiUing  horses  to  be  neutralized  by  the 
laggards. 

The  team  between  the  leaders  and  the  wheelers  is  called 
the  swing  team.  The  horse  on  the  left  of  each  team  is 
called  the  near  horse  and  that  on  the  right  the  off  horse. 


XXIV. — HORSE   AND   HARNESS. 


Requirements, 

The  preceding  considerations  illustrate  the  application  of 
the  principle  of  independence  of  function  to  meet  the  require- 
ments of  artillery  harness  which,  as  stated  by  another  writer, 
may  be  thus  abridged. 

"  No  horse  should  be  restrained  by  the  efforts  of  another, 
and  the  direction  of  the  traces  should  be  most  favorable  for 
draught.  The  drivers  should  be  able  to  harness  and  unhar- 
ness promptly,  by  night  as  well  as  by  day,  when  benumbed 
by  cold  and  when  excited  by  danger.  The  fall  or  loss  of  a 
horse  should  not  be  a  permanent  obstacle  to  the  advance, 
and  disabled  horses  should  be  easily  replaced. ' 

U.  S.  Artillery  Harness.    Figure  2. 

WHEEL    HARNESS. 

This  is  composed  of  four  essential  systems,  three  of  which 
occur  in  all  harnesses  except  for  horses  in  the  lead.  The 
systems  are  : 

1st.  The  head  gear  to  guide  and  hold  the  horse. 

2nd.  The  saddle  to  transport  the  driver,  who,  for  the 
independent  control  of  his  team,  is  mounted. 

3rd.  The  draicght  harness  which  enables  the  horse  to  move 
the  carriage  forward. 

4th.  The  breeching  for  moving  it  backward. 

1.  The  head  gear  consists  of  the  bridle  and  halter.  To 
the  bit  of  the  off  horse  is  attached  the  lead  rein,  one  end  of 
which  is  held  by  the  driver. 

2.  All  horses  are  saddled,  the  off  horse  carrying  the  driver's 
valise,  and,  when  necessary,  an  extra  cannoneer. 

3.  The  draught  harness  and  the  breeching  constitute  two 
independent  systems  symmetrically  arranged. 

The  former  is  composed  of  the  following  parts. 
The  hameSj  h,  figure  2,  are  two  curved  irons  shaped  like 
the  signs  ( ).     They  are  connected  together  below  by  an 


XXIV. — HORSE    AND    HARNESS. 


iron  clasp,  and  adjusted  at  the  top  by  a  leather  strap  so  as  to 
embrace  the  neck  and  form  a  rigid  frame  against  which  the 
horse  may  thrust.  To  diminish  the  pressure  per  unit  of  area 
on  the  horse's  shoulder*  the  hames  rest  on  a  similarly 
shaped  cushion,  the  collar.  To  each  hame  is  attached  by  a 
flexible  hinge  a  stout  leather  tug^  t.  This  terminates  in  an 
iron  ring  through  which  passes  the  trace  chain,  c^  terminated 
by  the  toggle^  t' .  The  latter  connects  the  front  trace  chain 
of  the  wheel  horse  with  the  rear  trace  chain  of  his  leader, 
and  so  on  throughout  the  column.  When  in  motion,  the  tug 
ring  plays  on  the  trace  chain  and  thus  makes  the  leading 
horses  independent  of  those  in  rear. 

The  length  of  the  rear  trace  chain  may  be  varied  by  a 
toggle  to  suit  the  conformation  of  the  horse. 

The  safe,  s,  protects  the  shoulder  from  chafing. 

The  loin  strap,  /,  sustains  the  trace  when  relaxed,  and  the 
belly  band  beneath  the  saddle  keeps  it  from  rising  over  the 
back  in  turning. 

4.  The  breeching  is  composed  of  the  broad  breech  strap, 
b,  figure  3,  corresponding  to  the  collar ;  it  is  supported  by 
the  hip  straps  h.  Corresponding  to  the  traces  is  a  Y-shaped 
system  consisting  :  —  1st.  Of  the  continuous  breast  strap,  bs, 
which,  passing  around  the  breast,  is  united  at  each  end  to  the 
breech  strap.  It  is  supported  in  front  by  iron  Hnks  hanging 
from  the  hames.  2nd.  The  stem  of  the  Y  is  formed  by  the 
pole  strap,  p,  connected  at  one  end  to  the  breast  strap  by  an 
iron  double-loop,  shaped  like  a  figure  8,  and  leading  obliquely 
downward  and  inward  to  the  end  of  the  pole.  The  functions 
of  the  pole  thus  correspond  to  those  of  the  splinter  bar 
in  rear. 


*  This  end  is  served  in  modern  practice  by  using  hames  of  sheet  steel 
formed  to  fit  the  shoulder.  The  same  principle  is  applied  in  the  cavalry 
saddle. 


XXIV. — HORSE   AND    HARNESS. 


Pole   Yoke, 

The  weight  of  the  pole  is  supported  by  the  pole  yoke, 
which  is  connected  by  a  short  chain  to  the  clasp  of  the 
hames.  The  branches  of  the  yoke  are  so  hinged  to  a  collar 
revolving  loosely  around  the  pole  that  they  can  play  only  in 
a  plane  passing  through  the  axis  of  the  pole. 

This  allows  the  horses  to  travel  freely  at  different  levels 
and  prevents  the  lateral  thrashifig  of  the  pole. 

LEAD    HARNESS. 

The  leading  horses  have  longer  traces  than  the  wheelers 
and  have  no  breeching;  otherwise  their  harness  is  identical. 

Improved  Harness.    Figure  4. 

The  harness  devised  by  Major  Williston  of  the  Artillery, 
which  is  now  undergoing  trial,  resembles  that  above  described 
except  in  the  following  principal  points. 

1st.  For  interchangeability,  the  saddles  and  bridles  are 
the  same  as  those  used  by  the  cavalry,  and  saddle  bags 
replace  the  valise. 

2nd.  The  wheel  traces  are  attached  to  single  trees  which 
may  be  hooked  to  the  saddle  when  not  in  use. 

3rd.  The  breeching  is  that  used  in  commerce.  The  stem 
of  the  Y  passes  under  the  horse  to  a  transverse  bar  in  front, 
which  corresponds  to  the  evener,  and  is  called  the  neck  yoke. 

This  is  the  most  important  change  from  the  regulation 
harness.  It  prevents  the  breech  strap  from  slipping  upward 
in  stopping  suddenly,  and  also  avoids  the  oblique  thrust  on 
the  horse's  neck  which  tends  to  make  him  fall. 

The  neck  yoke  also  controls  the  pole  better  than  the  hinged 
pole  yoke. 

4th.  The  bridle  rein  of  the  off  horse  passes  through  a 
pulley  on  his  saddle,  so  that,  in  holding  him  back,  the 
oblique  stress  above  mentioned  is  further  avoided. 


XXIV. — HORSE    AND    HARNESS. 


5th.  The  collar,  instead  of  being  continuous,  is  hinged 
above  and  is  provided  with  a  fastening  below  in  easy  reach. 

6th.  The  horse  of  the  chief  of  piece  is  provided  with  a 
light  draught  harness,  consisting  of  a  breast  collar  and  traces, 
with  which  in  an  emergency  the  other  horses  may  be  assisted. 
When  not  in  use  the  traces  are  folded  across  the  horse's 
withers. 

This  harness  is  distinguished  for  the  ease  with  which  the 
horses  may  be  detached  from  the  carriage  in  all  conditions  of 
service. 

LEATHER. 

That  used  in  harness  is  classified  according  to  its  thickness, 
into  harness," bridle  and  collar  leather. 

The  leather  from  the  necks,  shanks,  flanks  and  bellies,  or 
the  offal,  figure  5,  is  rejected  as  too  spongy  for  use,  so  that 
only  about  one-half  of  the  hide  is  employed.  Of  this,  the 
butt  is  the  best  portion. 

The  lighter  hides  are  slit  axially  into  sides. 


XXV. — ARTILLERY   MACHINES. 


CHAPTER  XXV. 

ARTILLERY  MACHINES. 
Object- 

Artillery  machines  are  employed  to  mount  and  dismount 
cannon  and  to  transport  artillery  material  from  one  part  of  a 
work  to  another.  They  comprise  the  gin,  the  gun  lift  and 
Jacks  of  various  forms;  and  wheeled  vehicles  such  as  the  sling 
cart,  the  truck,  etc. 

Machines  Used  in  Mounting  Cannon. 

The  gin  consists  of  a  tripod  composed  of  two  legs  which 
form  a  shear  or  derrick,  and  a  pry  pole  by  which  the  legs 
are  lifted  and  braced. 

The  hoisting  apparatus  consists  of  a  block  and  fall  sus- 
pended from  the  apex  and  operated  by  a  windlass  supported 
by  the  legs  in  a  position  convenient  for  the  use  of  handspikes. 

The  use  of  the  gin  is  confined  to  relatively  light  weights. 
Heavy  weights  are  preferably  lifted  by  the  hydraulic  jack  and 
loose  blocking. 

The  hydraulic  jack  is  a  compact  form  of  the  hydraulic 
press,  which  contains  within  itself  the  reservoir  of  liquid 
required.  It  is  provided  with  valves  by  which  the  direction 
of  the  motion  of  the  ram  may  be  varied. 

Other  jacks  apply  the  principles  of  the  lever  and  the  screw, 
and  are  correspondingly  named. 

The  gun  lift  consists  of  two  massive  trestles  so  framed  that 
they  may  be  easily  dismounted  for  transportation. 

Each  trestle  carries  on  its  beam  a  hydraulic  jack ;  the  latter 
by  means  of  a  lever  raises  a  bar  of  iron  which  passes  verti- 
cally through  the  beam  and  the  lever,  between  the  jack  and 
the  fulcrum  of  the  lever.  This  bar  is  pierced  at  short  inter- 
vals by  holes,  and  its  lower  end  is  formed  into  a  hook. 


XXV. — ARTILLERY   MACHINES. 


Both  bars  having  been  attached  to  the  weight,  and  a  pin 
having  been  passed  through  the  hole  in  the  bar  next  above 
the  lever,  the  ram  of  the  jack  is  raised  to  its  full  extent.  A 
pin  is  then  inserted  through  the  hole  next  above  the  beam 
and  the  ram  is  lowered.  The  upper  pin  is  then  shifted  down- 
ward and  the  operation  continued. 

For  comparatively  light  weights  a  single  trestle  may  be 
employed  like  a  gin. 

Machines  Used  in  Transportation. 

Heavy  weights  are  usually  transported  by  the  aid  of  cap- 
stans and  rollers. 

When  space  permits,  cannon  may  be  rolled  bodily  by  par- 
buckling. In  such  cases  a  muzzle  collar  of  the  maximum 
diameter  of  the  piece  corrects  the  circular  path  which  the 
conical  mass  tends  to  describe. 

Heavy  weights  may  also  be  rolled  through  the  narrow 
passages  of  forts  on  a  low  framework  called  the  cradle. 

The  wheels  of  sling  carts  are  large  and  have  but  little  dish. 
Since,  hke  the  gin,  they  suspend  the  load,  they  are  relatively 
weak,  and  hence  are  used  for  lighter  weights  than  the  cradle. 

By  mechanical  appliances  mounted  on  the  axle,  the  weight 
may  be  lifted  from  the  ground,  and  during  transportation 
may  be  permanently  secured  to  the  axle  by  hooks  which 
relieve  the  more  delicate  mechanism  from  shocks. 

The  means  of  lifting  are  the  screw,  and  the  hydraulic  jack 
which  works  on  the  principle  explained  for  the  gun  lift. 

For  light  weights  the  eccentric  position  of  the  hooks  may 
enable  the  weight  to  be  raised  by  lifting  the  pole  before  the 
weight  is  attached  and  afterwards  by  depressing  it.  This 
means  of  lifting  is  applied  to  the  iron  sling  cart.  The  field 
limber  may  be  similarly  used  to  carry  a  piece,  the  carriage  of 
which  is  disabled. 

In  transportation  the  pole  of  the  sling  cart  is  supported  by 
the  limber. 


XXVI. — HAND    ARMS. 


CHAPTER  XXVI. 

HAND  ARMS. 

The  weapons  carried  by  the  soldier,  or  portable  arms  may 
be  divided  into  hand  arms  and  small  arms. 

The  former  class  is  known  in  French  as  '^armes  blanches ; " 
the  latter  requires,  as  in  cannon,  a  preliminary  study  of  the 
ammunition  employed.     See  Chapter  XXVII. 

Classification. 

Hand  arms  are  divided  into 

1st.  Thrusting  arms  which  act  by  the  point. 

2nd.  Cutting  arms  which  act  by  the  edge. 

These  functions  may  be  combined  in  the  same  weapon, 
though  at  some  sacrifice  of  efficiency. 

Thrusting  Arms. 

The  body  of  a  thrusting  weapon  should  be  straight  so  as 
to  avoid  a  rotary  moment  on  impact,  and  the  center  of  gravity 
should  be  placed  near  the  handle.  This  may  be  attained  by 
fluting  the  blade,  or  by  suitably  weighting  the  handle. 

The  principal  thru^sting  weapons  are  the  straight  sword,  the 
lance  and  the  bayonet. 

The  sword  is  composed  of  the  blade,  the  hilt  by  which  it 
is  held,  and  the  guard.  A  knob  sometimes  acts  to  counter- 
poise the  blade  as  in  the  foil. 

The  lance  is  composed  of  a  short  steel  blade  fixed  to  the 
end  of  a  wooden  handle  about  10  to  16  feet  in  length.  The 
handle  is  furnished  with  a  leather  arm-loop  placed  over  the 
center  of  gravity. 


XXVI. — HAND    ARMS. 


After  a  long  period  of  comparative  disuse,  in  spite  of  the 
greatly  increased  efficiency  of  small  arms,  its  use  abroad  is 
now  becoming  more  general.  In  this  country  it  has  never 
been  successfully  employed. 

The  bayonet  is  useful  principally  for  guard  duty  and  for 
its  moral  effect.  Like  other  hand  arms,  it  has  the  merit  of 
"never  missing  fire." 

The  objections  attending  its  weight  and  that  of  its  scab- 
bard, and  its  eccentric  position  in  firing  may  be  partly  over- 
come by  combining  its  functions  with  those  of  the  ramrod. 
Attempts  have  also  been  made  to  turn  it  into  an  intrenching 
trowel.  The  tendency  is  now  to  shorten  it  to  the  proportions 
of  a  dirk,  which  may  form  a  useful  knife. 

Cutting  Arms. 

The  efficiency  of  these  arms  is  promoted  by  increasing  the 
distance  of  the  center  of  gravity  from  the  handle,  and  by  giv- 
ing a  curvature  to  the  cutting  edge  so  as  to  develop  on  impact 
a  tangential  or  slicing  component  which  will  call  into  play 
the  serrated  edge  possessed  by  even  the  sharpest  knife.  This 
enables  the  weapon  to  rupture  in  detail  the  muscular  fibers 
on  which  it  acts. 

Description. 

The  principal  cutting  weapon  is  the  saber.  Sabers  are 
classified  according  to  their  use.  In  the  U.  S.  service  there 
are  two  kinds,  viz.  :  the  cavalry  saber  and  that  for  the  light 
artillery. 

The  cavalry  saber,  being  used  on  horseback  for  thrusting  as 
well  as  for  cutting,  has  but  a  slight  curvature,  a  long  blade, 
and  a  basket  hilt  (properly  a  guard)  which  carries  the  center 
of  gravity  toward  the  handle. 

The  light  artillery  saber  being  intended  for  hand  to  hand 
conflict  by  troops,  who  for  the  service  of  their  batteries  are 


XXVI. — HAND   ARMS. 


dismounted,  is  shorter  than  the  cavalry  saber,  is  more  curved, 
and  has  a  guard  composed  of  a  single  scroll  of  brass. 

Remarks. 

The  present  tendency  is  to  make  the  artilleryman  depend 
for  his  personal  defence  upon  the  gun  which  his  duty  to  the 
other  troops  compels  him  to  serve  to  the  very  last  extremity. 
He  should  therefore  be  free  from  any  incumbrance  which 
will  distract  him  from  his  proper  functions. 

In  order  to  avoid  the  exposure  of  the  person  in  cutting, 
many  cavalry  officers  are  in  favor  of  avoiding  the  objections 
to  the  combined  functions  of  the  cavalry  saber  by  using  it 
solely  for  thrusting. 

On  the  other  hand  the  swordsmen  of  East  India,  than 
whom  there  are  few  more  expert,  prefer  blades  which  are 
greariy  curved,  the  radius  of  curvature  of  some  being  about 
18  inches. 

The  following  discussion  illustrates  the  effect  of  curvature, 
frequently  utilized  in  the  useful  arts. 


^  "-V       s'  ^'"' 

Let  O  S Ph^  the  edge  of  a  curved  blade  rotated  around 
O  and  striking  at  P  with  a  blow,  P  F,  at  right  angles  to 
OP,  ThenP  T=PPcQS(p  =PF  cos  i^  Z' r  is  the  tan- 
gential component,  and  this  will  be  measured  by  P  P  cos 
C  P  Oj  which  gives  an  easy  method  of  discussing  the  effect 
of  curvature.     If,  as  in  the  artillery  saber,  S',  the  radius  of 


XXVI. — HAND    ARMS. 


curvature,  be  shortened  by  placing  the  center  at  C  ;  or,  if 
as  in  some  Eastern  blades  which  have  a  tangential  handle  and 
also  in  the  common  scythe,  the  center  of  rotation  be  placed 
above  the  line  P  O,  the  value  of  cos  (p  will  be  increased  and 
so  will  the  proportionate  value  of  the  tangential  component. 
On  the  other  hand  if,  as  in  the  cavalry  saber,  the  handle 
be  lowered  as  to  O,  in  order  to  increase  the  tangential  com- 
ponent in  thrusting,  the  slicing  component  will  decrease. 


XXVII. — SMALL   ARM   AMMUNITION. 


CHAPTER  XXVII. 

SMALL  ARM  AMMUNITION. 

The  Eelation  between  Arms  and  Ammunition. 

As  seen  in  Chapter  V,  the  efficiency  of  all  fire  arms  has 
been  dependent  principally  upon  the  nature  of  their  ammu- 
nition. 

This  may  be  called  the  food  of  the  gun  as  the  means  of 
conveying  it  to  the  chamber  is  actually  called  the  feed.  As 
a  rule  the  gun  must  be  made  to  fit  the  ammunition  as  a  shoe 
should  be  made  to  fit  the  foot. 

MUZZLE    LOADING    AMMUNITION. 

Powder  and  ball  were  originally  carried  loose;  but  for 
some  time  the  greater  rapidity  of  fire  with  arrows  at  the 
ranges  common  to  both  weapons,  caused  the  latter  to  be 
preferred. 

Gustavus  Adolphus  made  important  improvements  in  the 
ammunition. 

He  first  provided  separate  receptacles  for  each  powder 
charge ;  these  were  called  cartridges  from  their  paper 
envelopes.     (Latin  charfa,  paper.) 

He  subsequently  combined  the  powder  with  the  projectile 
in  the  paper  wrapper,  which,  until  about  1865,  formed  the 
principal  ammunition  for  small  arms.     See  Figure  1. 

In  addition  to  the  comparative  disadvantages  of  muzzle 
loading  arms  cited  in  Chapter  XI,  may  be  named  the  vari- 
able amount  and  condition  of  the  powder  in  the  chamber, 
since  the  powder  was  but  imperfectly  protected  from  moist- 
ure and  was  hable  to  be  wasted  in  loadmg.     There  was  also 


XXVII. — SMALL   ARM   AMMUNITION. 


the  danger  of  inadvertently  loading  tlie  piece  with  more 
than  one  cartridge  at  a  time.  Nearly  one-half  of  the 
muskets  abandoned  at  the  battle  of  Gettysburg  were  found 
to  contain  more  than  one  cartridge. 

In  spite  of  the  theories  of  those  who  feared  that  increased 
rapidity  of  fire  would  lead  to  a  disastrous  expenditure  of 
ammunition,  there  has  always  been  the  feeling  expressed  by 
Frederick  the  Great  in  saying,  that  other  things  being  equal, 
"  He  who  fires  fastest  hits  most." 

BREECH    LOADING    AMMUNITION. 

Non-metallic  Ammunition. 

The  state  of  the  arts  required  the  first  breech  loading 
ammunition  to  be  formed  after  the  manner  of  that  just 
described ;  and,  as  it  was  impossible  to  permanently  prevent 
the  escape  of  gas  by  the  close  fitting  of  the  parts  of  the 
breech,  the  joint  required  for  rapid  loading  was  generally 
placed  in  front  of  the  chamber,  from  which  position  the 
soldier  would  suffer  least  from  the  discharge. 

To  facilitate  loading  the  section  of  the  barrel  containing 
the  chamber  was  caused  to  oscillate  about  an  axis  in  rear; 
so  that,  the  paper  cartridge  having  been  broken  for  loading, 
the  bullet  acted  as  a  stopper  to  prevent  the  exposure  of  the 
loose  powder  before  the  piece  was  closed. 

This  structure  distinguishes  a  large  class  of  arms,  now 
obsolete,  which  are  known  as  having  7novable  chambers. 
This  includes  the  Hall  rifle,  used  in  this  country  in  the  early 
part  of  the  century.  It  is  believed  to  be  the  first  breech 
loading  small  arm  used  by  troops. 

The  operation  of  such  guns  was  necessarily  slow  and 
defective. 

METALLIC    AMMUNITION. 

Origin. 

The  primed  metallic  cartridge  case,  invented  in  France, 
was  first  used  by  troops  during  our  Civil  War.     It  contained 


XXVlt. — SMALL   ARM   AMMUNITION. 


all  the  components  of  the  ammunition,  under  invariable  con- 
ditions, in  an  envelope  which  formed  a  gas  check,  and  was 
therefore  adapted  to  arms  in  which  the  chamber  was  fixed. 

Being  rigid  and  of  exact  dimensions  it  could  be  and  was 
at  first  most  extensively  used  in  magazine  arms,  in  which 
the  operations  of  loading  are  automatically  performed. 

Rim  Fire. 

In  order  to  support  it  against  the  blow  which  exploded  the 
fulminating  priming,  and  to  extract  the  empty  case,  it  was 
provided  with  a  rim.  For  simplicity  of  manufacture,  and 
because  the  arms  in  which  it  was  principally  employed  con- 
tained the  cartridges  in  tubular  magazines  and  were  carried 
by  mounted  troops,  the  fulminate,/,  was  placed  within  the  rim, 
as  shown  in  figure  2. 

This  construction,  although  confusing  the  functions  of  the 
rim  and  the  primer,  was  intended  to  prevent  accidental  ex- 
plosions in  the  magazine. 

For  the  small  charges  of  powder  then  used,  the  metal  could 
be  made  thin  enough  for  certainty  of  fire,  since  it  was  com- 
posed of  soft  copper. 

Figure  2  shows  that  such  a  cartridge,  having  what  is  termed 
a  folded  head,  is  necessarily  unsupported  by  the  walls  of  the 
chamber  for  a  length  at  least  equal  to  the  thickness  of  the 
metal  forming  the  rim.  Consequently,  as  charges  and  pres- 
sures were  increased,  the  rim  fire  cartridges  were  found  to 
shear  across  the  edge  of  the  chamber ;  and  the  copper  was  so 
deficient  in  elasticity  that  they  would  resist  extraction. 

The  quantity  of  fulminate  contained  in  the  rim  was  much 
greater  than  was  required  for  ignition  at  any  one  point,  and 
further  tended  to  destroy  the  fold.  The  distribution  was  im- 
perfect and  misfires  were  frequent. 

The  cartridge  could  not  be  reloaded. 


XXVII. — SMALL   ARM    AMMUNITION. 


Central  Fire. 

As  metallic  ammunition  became  more  generally  employed 
in  all  arms,  these  objections  led  to  the  use  of  the  center  fire 
cartridge,  now  universally  employed ;  these  objections  led 
also  for  a  time  to  the  disuse  of  magazine  arms. 

The  adoption  of  central  fire  permits  the  case  to  be  strength- 
ened indefinitely  in  the  shearing  plane ^  and  to  be  made  of 
an  elastic  material  like  brass,  the  special  elasticity  of  which, 
developed  by  its  manufacture,  facilitates  its  extraction.  It 
also  permits  the  reloading  required  by  the  great  expenditure 
of  ammunition  m  target  practice. 

Folded  Head. 

The  first  center  fire  cartridges  were  made  with  folded  heads, 
as  the  arts  then  furnished  no  other  method  of  forming  the  rim. 
To  avoid  shearing,  a  thin,  cup-shaped,  gas  check,  as  shown  in 
figure  3,  was,  and  is  still  employed.  This  contains  a  central 
hole  to  allow  the  flame  from  the  fulminate,  /,  to  pass  through 
the  vents,  vv^  in  the  anvil,  a. 

The  Ordnance  Department  for  several  years  made  the  copper 
cup-anvil  cartridge  shown  in  figure  4.  In  this  it  was  attempt- 
ed to  combine  in  one  piece  the  functions  of  the  gas  check 
and  of  the  anvil.  But  these  were  inconsistent,  and  the  cart- 
ridge, although  avoiding  objections  urged  against  a  per- 
forated head  which  contained  a  loose  primer,  was  abandoned. 

The  limit  of  resistance  to  shearing  was  soon  reached, 
because,  owing  to  the  manufacture,  the  maximum  thickness  of 
metal  is  that  of  the  head.  So  that  if  a  thicker  or  more  elastic 
metal  was  used  misfires  would  result,  unless  the  energy  of  the 
blow  required  for  ignition  was  so  much  increased  that  the 
rapidity  of  fire  was  diminished. 

The  flat  anvil,  figure  5,  demanded  by  the  obhque  firing 
pin  of  the  Springfield  rifle,  requires  a  more  powerful  blov/ 
than  does  that  shown  in  figure  3,  and  the  thickness  of  metal 


XXVII. SMALL    ARM    AMMUNITION. 


requires  the  firing  pin  to  be  sharp.  On  the  other  hand,  the 
anvil  of  figure  3  is  well  adapted  to  the  axial  blow  of  a  flat 
pointed  pin.  This  requires  less  work  in  cocking  and  is  less 
apt  to  pierce  the  cap. 

Solid  Heads. 

The  state  of  the  arts  now  permits  the  U.  S.  cartridge  to  be 
made  with  a  solid  head,  as  in  figure  5.  The  shearing  plane 
lies  in  front  of  the  edge  of  the  chamber  even  when,  owing  to 
the  yielding  of  its  support,  the  case  may  be  forced  backward 
in  firing. 

Certainty  of  ignition  now  requires  that  the  anvil  shall  be 
renewed  at  every  fire.  Consequently  the  primer  is  assembled 
before  issue  with  its  anvil  and  fulminate  complete.  The 
resulting  variation  in  figure  3  is  shown  in  figure  6. 

An  objection  to  the  solid  head  cartridge  arises  from  its  un- 
equal expansion  when  fired.  The  mouth,  being  thin,  is  more 
firmly  held  by  friction  against  the  walls  of  the  chamber  than 
is  the  thicker  portion  in  rear,  so  that  the  latter  may  slide 
backward  to  the  extent  permitted  by  its  support.  Cases 
which  have  been  often  reloaded  are  found  to  tear  across  by 
longitudinal  stress. 

The  Morse  cartridge,  figure  7,  provides  for  this  by  making 
the  head  entirely  separate  from  the  body  of  the  case. 

Remark, 
The  influence  of  improvements  in  metallic  ammunition  has 
probably  reached  its  limit  in  the  cartridge  employed  in  rapid 
firing  cannon,  Chapter  XXIX,  page  18.  The  size  of  the 
cartridges  which  these  employ  is  limited  by  the  weight  which 
one  man  can  conveniently  handle. 

METALS  USED  FOR  CARTRIDGE  CASES. 

Copper  was  first  employed  on  account  of  the  ease  with 
which  it  could  be  worked.     When  alloyed  with  a  small  pro- 


XXVn. — SMALL   ARM    AMMUNITION. 


portion  of  zinc  it  was  until  recently  preferred  by  the  U.  S.  to 
brass,  which,  when  in  contact  with  gun  powder,  undergoes  in 
time  a  molecular  change  that  renders  it  as  brittle  as  baked 
clay.  It  is  said  that  the  discovery  of  this  defect  in  the 
Russian  ammunition  postponed  the  war  of  1877. 

The  deficient  elasticity  of  copper  accounts  for  the  preva- 
lence of  the  lever  used  for  extraction  in  early  breech  loading 
arms,  and  for  their  comparative  slowness  of  fire. 

Brass  is  cheap  and  so  elastic  that  guns  in  which  it  is  used 
may  be  opened  by  the  direct  action  of  an  axial  bolt.  For 
the  reasons  given,  Chapter  XXVIII,  page  6,  the  rapidity  of 
fire  of  such  arms  is  increased.  This  is  the  metal  now 
generally  employed.  In  order  to  protect  it  from  the  powder 
the  cavity  may  be  varnished  or  tinned. 

The  elasticity  of  brass  adapts  it  to  reloading  since  resizing 
is  less  necessary  than  with  copper. 

The  operation  of  resizing  is  required  by  unavoidable  dif- 
ferences in  the  chambers  of  different  guns.  The  brass  cart- 
ridges used  in  the  rifle,  Cal.  0.45  may  often  be  reloaded  for 
use  in  the  same  gun  without  resizing  them  ;  but  owing  to  the 
greater  pressures  found  in  the  new  Cal.  0.30  rifle,  firing  smoke- 
less powder,  resizing  is  always  required  for  this  arm.  See 
Chapter  XXVIII,  page  3. 

Low  steely  when  protected  from  oxidation,  is  proposed  as  a 
cartridge  metal,  on  account  of  its  strength  elasticity  and 
freedom  from  structural  change. 


MANUFACTURE  OF  METALLIC  AMMUNITION. 

The  cartridge  case  may  be  made  in  two  general  ways, 
viz. :  1st,  by  coiling  by  hand  a  thin  sheet  of  metal  into  a 
tube ;  2nd,  by  drawing  the  tube  from  a  thicker  disc  as  de- 
scribed in  Chapter  XVIII,  page  2. 


XXVII.— SMALL   ARM    AMMUNITION. 


1.  Wrapped  Metallic  Cartridges.   Chap.  XVI,  figure  8 

The  metallic  sheet  is  trapezoidal  so  as  to  increase  the 
thickness  of  the  walls  near  the  head.  This  gives  the  ex- 
terior the  conical  form  required  for  extraction,  while  the 
interior  being  cylindrical  retains  its  hold  on  the  bullet.  It 
also  increases  the  thickness  of  the  flange  by  which  the 
case  is  riveted  to  Ihe  separate  disc  that  forms  the  head. 

This  method,  the  origin  of  which  is  evident,  avoids  the 
use  of  the  expensive  machinery  used  in  the  second  process, 
so  that  in  an  emergency  the  manufacture  could  be  easily 
improvised. 

The  cartridge  is  serviceable,  but  neither  waterproof,  rigid, 
nor  exact  enough  in  its  dimensions,  for  all  the  requirements 
of  service. 

2.  Drawn  Cartridges. 

The  operation  of  drawing  necessarily  leaves  the  exterior 
of  the  tube  cylindrical,  so  that  the  required  variation  in 
thickness  is  obtained  by  varying  the  diameter  of  the 
punch. 

The  primary  draws  are  facilitated  by  removing  by  an- 
nealing, (/.  ^.,  heating  followed  by  quenching),  the  special 
elasticity  developed  by  the  previous  operations.  Chapter 
XV,  page  22. 

After  having  been  drawn  to  a  length  slightly  in  excess  of 
that  required,  the  tubes  are  trimmed  to  an  exact  length  to 
prepare  them  for  the  operations  of  heading. 

The  mandrel,  figure  8,  supports  the  trimmed  case  in  a 
closely  fitting  die.  A  hunter  of  the  proper  dimensions  first 
forms  the  pocket  for  the  primer,  and  a  second  operation  with 
a  bunter,  such  as  shown,  causes  the  metal  to  flow  into  the 
annular  space  provided  for  the  rim.  The  pocket  is  then 
vented. 


XXVII. — SMALL   ARM    AMMUNITION. 


To  facilitate  extraction  the  case  is  tapered  by  forcing  over 
it  a  conical  die.  The  cylindrical  seat  for  the  bullet  is 
simultaneously  formed. 

Components 

The  U,  S.  atwil  is  made  from  a  copper  wire  of  rectangular 
cross  section  containing  on  one  side  a  continuous  groove. 
From  this  are  punched  a  series  ot  circular  discs  which  form 
the  anvils,  The  edges  of  the  discs  are  notched  so  as  to 
form  a  passage  way  for  the  flame  of  the  fulminate,/,  through 
the  notches,  into  the  groove  which  bridges  over  the  vent,  z/,  in 
the  head  of  the  cartridge. 

The  bullet  is  composed  of  an  alloy  ot  lead  and  tin ;  the 
latter  metal,  although  it  increases  the  difhculty  of  manufac- 
ture, gives  the  hardness  required  to  resist  deformation  in 
the  gun.     Chapter  XXVIII,  page  3. 

The  bullet  is  made  by  compression  between  dies  which 
part  on  an  axial  plane.  See  figure  9.  The  cavity  in  the 
base  of  the  bullet  may  be  varied  to  bring  the  bullets  to  an 
exact  weight. 

The  bullet  is  lubricated  by  being  forced  through  a  vege- 
table wax  so  as  to  fill  the  cannelures,  or  grooves.  This  is 
preferred  to  a  fat,  as  it  does  not  corrode  the  metals  in  store. 

Common  Operations 

In  the  loading  machine  a  measured  charge  of  powder  is 
first  deposited  in  the  case  and  slightly  compressed  so  as  to 
increase  the  density  of  loading.  The  bullet  is  next  inserted 
and  secured  by  crimping  the  case  upon  it. 

The  finished  cartridges  are  all  inspected  for  weight  and 
dimensions. 

The  first  is  accomplished  by  a  weighing  machine  which 
rejects  all  that  weigh  less  than  a  prescribed  minimum.  The 
principal  object  of  this  operation  is  to  detect  charges  in- 


XXVII. — SMALL   ARM    AMMUNITION.  0 

sufficient  to  expel  a  projectile  which  might  cause  a  subse- 
quent discharge  to  burst  the  gun. 

The  gauging  machine  makes  sure  that  every  cartridge 
will  enter  the  gun.  The  gauging  die,  which  is  sUghtly 
smaller  than  the  minimum  chamber,  verifies  the  length  of 
the  cartridge  to  the  rear  from  the  circle  of  contact  between 
the  bullet  and  the  rifling,  the  profile  between  these  planes, 
and  the  maximun  radius  of  the  rim. 

For  safety  the  primer  is  sunken  below  the  plane  of  the 
head. 

The  automatic  operation  of  the  machinery  has  greatly 
reduced  the  cost  of  manufacture,  and  has  thus  removed  one 
of  the  principal  objections  to  metallic  ammunition. 

The  inspection  merely  precedes  the  proof.  Chapter 
XVII,  page  18.  This  consists  in  firing  a  portion  of  the 
daily  product  to  verify  the  certainty  of  fire,  the  strength  of 
the  case,  to  determine  the  volume  of  the  charge,  the  com- 
pression required  for  the  standard  velocity  and  above  all  to 
test  the  accuracy  of  fire. 

U.  S.  SMALL  ARM  AMMUNITION. 

The  following  varieties  are  now  made  (1891) : 

1.  The  rifle  ball  cartridge,  /^^q,  or  about  70  grains  of 
powder  and  a  500  grain  bullet.     /  V=  1280  /  s. 

2.  The  carbine  ball  cartridge,  /o\-     ^  ^-=  1150  /  s, 

3.  The  revolver  ball  cartridge,  f^^.     I  V=  730 /j-. 

4.  The  rifle  and  carbine  blank  cartridge,  filled  with  com- 
pressed powder  that  is  protected  by  a  varnished  paper  cup, 
and  retained  by  crimping  the  case  so  as  to  facilitate  loading. 

5.  The  revolver  blank  cartridge  as  in  4. 

Important  changes  in  this  ammunition  are  now  pending. 
Their  principles  will  be  hereafter  discussed  in  connection 
with  the  arm.  It  is  significant  to  observe  that  now,  as  here- 
tofore, the  adoption  of  the  new  arm  awaits  the  perfection  of 
its  ammunition.     Chapter  XXVIII,  page  19. 


XXVIII. — SMALL    ARMS. 


CHAPTER  XXVIII. 

SMALL  ARMS. 
Classification. 

Small  arms  may  be  classified  according  to  the  service  in 
which  they  are  employed,  as  this  determines  the  maximum 
length  of  barrel,  given  to  the  rifle^  i\\Q  carbine^  and  W^q  pistol. 

Muzzle-loading  arms,  and  breech-loaders  having  movable 
chambers  being  now  obsolete,  breech-loading  small  arms 
with  fixed  chambers  may  be  classified  into  single  loading  and 
magazine  arms. 

The  latter  class  is  now  supplanting  the  former,  because  of 
the  moral  and  physical  advantage  of  being  able  at  will  to 
increase  the  rapidity  of  musketry  fire. 

Historical  Sketch. 

Some  of  the  objections  formerly  made  against  the  breech- 
loader have  been  discussed  in  Chapter  XXVII.  To  these  may 
be  added  the  former  fear  that  the  mechanism  might  not  endure 
the  accidents  of  service. 

But  the  Prussian  wars  of  1864  and  1866,  and  the  more 
extended  campaigns  of  1870,  proved  that  after  a  victory 
there  is  generally  time  enough  for  repairs. 

During  the  siege  of  Plevna  in  1877,  these  conclusions 
were  emphasized  by  the  use  by  the  Turks,  for  the  first  time 
in  Europe,  of  the  American  Winchester  repeater. 

Although  of  a  model  now  considered  imperfect,  its  success 
was  conclusive. 

It  is  now  realized  that  the  change  from  muzzle-loading  to 
breech-loading  having  established  the  advantages  of  rapidity, 
the  choice  of  a  magazine  arm  is  a  detail  to  be  determined  by 


XXVIII. — SMALL   ARMS. 


independent  considerations.  The  selection  is  attended  with 
many  complications  which,  as  in  the  past,  relate  principally 
to  the  ammunition.  Some  of  these  will  be  hereafter  dis- 
cussed in  detail »  but  it  may  be  premised  that,  while  the 
power  ol  the  weapon  depends  principally  upon  the  abiUty  of 
its  (human)  carriage  to  resist  recoil ;  its  continued  operation 
depends  upon  the  number  of  cartridges  which  this  carriage 
can  conveniently  transport. 

The  development  is  thus  limited  by  a  physical  constant. 

COMPONENT  PARTS  OF  B.  L.  SMALL  ARMS. 

I.     THE    BARREL. 

Weight. 

Except  for  considerations  relating  to  the  recoil  and  the 
practical  necessities  of  service,  the  general  use  of  steel  would 
permit  the  barrel  to  be  considerably  reduced  in  weight. 

Caliber. 

Although  the  best  results  follow  from  adapting  to  each  arm 
its  own  ammunition,  yet  in  order  to  meet  emergencies  the 
cartridges  for  the  rifle  and  the  carbine  may  be  interchanged. 
These  arms  are  therefore  of  the  same  caliber. 

For  the  reasons  stated  in  Chapter  XVI,  since  the  adoption 
of  the  rifle  principle  the  tendency  has  been  to  reduce  the 
caliber.  The  limit  is  fixed  by  questions  of  internal  ballistics, 
and  also  by  the  nervous  shock  communicated  to  the  animal 
struck.  Upon  the  shock  is  thought  to  depend  the  "  stopping 
power  "  of  a  bullet  that  does  not  kill. 

Until  lately  the  limit  was  generally  taken  at  about  0.45 
inch,  but  recent  experiments  have  induced  many  countries  to 
reduce  it  still  further  to  about  0.30  inch. 

The  propriety  of  the  change  is  still  debated,  and  like  many 
others  requires  the  test  of  war.  The  advantage  may  consist 
in  this :   that  a  shock  which  might  be  insufficient  to  stop  a 


XXVIII. — SMALL   ARMS. 


man  in  the  heat  of  a  close  action  may,  at  the  long  ranges 
which  the  reduced  caliber  provides,  be  severe  enough  to  cause 
him  to  withdraw.     But  this  would  not  apply  to  horses. 

Rifling. 

The  cross-section  of  the  rifling  depends  principally  on  the 
nature  of  the  bullet.     If  this  be  of  a  soft  material,  like  lead, 
the  lands  may  be  broad  as  in  the   Springfield  rifle  and  con 
versely,  figure  15,  if  the  metal  be  hard.     The  grooves  should 
be  shallow  and  so  formed  as  to  be  readily  cleaned. 

The  increase  of  spherical  density,  which  results  from 
reducing  the  diameter  of  a  projectile  of  which  the  length, 
and  therefore  the  sectional  density,  is  kept  nearly  constant, 
has  required  a  considerable  increase  in  the  twist,  so  that 
special  precautions  have  been  required  to  prevent  the  pro- 
jectile from  shearing.     Chapter  XVI,  page  10. 

In  the  caliber  0.45  bullet  this  was  done  by  alloying  the  lead 
with  tin,  Chapter  XXVII,  page  8 ;  the  new  bullet  is  more- 
over coated  with  a  thin  jacket  of  a  harder  metal.  Chapter 
XXVII;  Plates. 

II.    THE    STOCK. 

This  forms  the  handle  by  which  the  barrel  is  directed.  It 
is  made  of  wood  on  account  of  its  lightness  and  strength  and 
its  deficient  conductivity  of  heat. 

The  form  of  the  stock  depends  on  the  conformation  of  the 
average  man. 

The  butt  is  widened  and  curved  so  as  to  diminish  the 
pressure  per  unit  of  area  due  to  the  recoil.  It  is  bent  for 
convenience  in  aiming.  A  rotary  component  of  recoil  is 
thereby  developed,  which,  if  the  crook  be  excessive,  may 
cause  inconvenience  to  the  firer. 

The  stock  is  necessarily  weakened  by  being  cut  across  the 
grain  to  form  a  grasp,  and  more  so  by  the  present  develop. 


XXVIII. — SMALL   ARMS. 


ment  in  the  volume  of  the  parts  about  the  breech  It  is 
consequently  frequently  made  in  two  pieces,  the  ///  stock 
being  of  a  rigid  material,  such  as  black  walnut,  and  the  butt 
itoik  preferably  tough,  as  of  elm.     Chapter  XV,  page  12. 

The  support  m  rear  of  the  barrel  should  be  of  sufficient 
area  to  avoid  permanent  deformation;  and  that  beneath  the 
barrel  should  not  be  unduly  rigid,  since  otherwise  the  barrel 
may  be  distorted  by  the  effects  of  moisture  upon  the  wood. 


Ill      THE    SIGHTS. 

The  position  of  the  rear  sight  is  determined  by  the  limit  of 
distinct  vision,  and  is  so  taken  that  the  two  sights  and  the 
object  shall  collectively  be  most  plainly  seen. 

The  sights  are  separated  as  far  as  convenience  permits,  so 
as  to  rectify  their  ahgnment  with  the  object.  See  Chapter 
XXX,  page  7.  They  admit  of  a  permanent  correction  for 
jump  and  a  variable  correction  for  range,  drift  and  the  effects 
of  wind. 

The  increasing  flatness  of  the  trajectory  and  the  growing 
rapidity  of  fire  will,  except  for  sharpshooters,  probably 
diminish  the  number  of  adjustments  now  given  to  the  rear 
sight. 

It  is  probable  also,  that  instead  of  providing  an  extension 
to  the  slide  for  use  at  extreme  ranges,  a  separate  pair  of  sights 
will  be  placed  on  the  side  of  the  arm.  The  ordinary  func- 
tions of  the  members  of  this  pair  will  be  reversed;  that  is,  the 
rear  sight  will  be  fixed  and  the  front  sight  movable  down- 
ward, so  that  a  considerable  elevation  may  be  attained  with- 
out great  variation  in  the  relative  positions  of  the  eye  of  the 
marksman  and  the  point  of  his  body  which  receives  the  recoil. 

It  may  be  remarked  that  the  requirements  of  sights  for  war 
service  and  for  target  practice  at  kiiowti  distafices  are  in  many 
essentials  incompatible. 


XXVIII. — SMALL    ARMS. 


[V.    THE    MOUNTINGS. 


The  bands,  screws,  pins,  etc.,  are  intended  to  connect  the 
parts ;  and  the  butt  plate,  tip  and  the  extension  of  the  guard 
beneath  the  small  of  the  stock  are  intended  to  protect  from 
wear  and  to  strengthen  the  relatively  perishable  wood. 


Functions. 


V.    THE    BREECH    MECHANISM. 


The  functions  of  the  breech  mechanism  are  five,  viz.  :  to 
open,  load  and  lock  the  breech,  to  fire  the  charge,  and  to 
remove  the  empty  shell. 

The  manner  in  which  these  functions  are  performed 
depends  primarily  upon  the  manner  of  opening  and  closing 
the  breech,  as  is  shown  by  the  following  scheme  : 

Classification  of  B.  L.  Small  Arms.* 


o  2 

a>  ? 

u  ^ 


■5  « 

as 


Barrel, 
which 


slides 


b 


...2. 
...3. 


Breech 

block 

which 


rotates 

about  J  JUo  axis  of  gnn. 
an  axis  1  Lto  axis  of  gun. 
which  is  [ 

slides      I  Jltoaxis  of  gun 4. 

^^'"^^       1  Lto  axis  of  gun 5. 


f  1 1  to  axis  of  gun 6. 

fin  front  of  block  7. 


L  to  axis  . 
of  gun.  1 


not  in  front  of  1 
block.  I 


No.  Examples. 
(Rare). 


Revolvers  t 
Shot  guns. 


Bolt  guns. 
Sharps,  (Krupp). 

Joslyn,  Warner. 
( Springfield, 
I  Remington. 

Martini. 


,  movable  chambers  (obsolete) 9.  Hall,    Burnside. 


Discussion  of  Table. 

The  mass  of  the  barrel  renders  the  classes,  1,  2,  3,  unsuit- 
able for  the  military  service  except  when,  as  in  revolvers,  the 
mass  is  greatly  reduced. 


*  For  a  fuller  discussion,  see  Report  Chief  of  Ordnance,  1873. 

t  The  classification  ot  these  is  difficult.  For  some  reasons  they  may 
be  considered  as  movable  chambers,  and  in  other  respects  they  may  be 
considered  as  an  aggregation  of  barrels  of  reduced  length. 


XXVIII. — SMALL   ARMS. 


Classes  5,  6,  8,  are  objectionable,  as  their  operation  does 
not  assist  in  loading  the  cartridge,  but  rather,  as  the  French 
say,  to  guillotine  it. 

They  possess,  however,  the  advantage  of  naturally  resisting 
the  pressure  which  tends  to  blow  open  the  breech  or  to 
"  unlock''  it. 

Class  7  naturally  forms  a  lever,  formerly  useful  in  forcing 
into  the  chamber  a  deformed  cartridge  or  in  extracting  one 
that  stuck.  Arms  of  classes  4,  5  and  8  were  frequently  pro- 
vided with  levers. 

Bolt  System. 

But,  as  the  quality  of  the  ammunition  has  improved,  the 
arms  of  class  4  7vithout  levers^  have  grown  mto  general  use. 

The  following  are  the  principal  objections  which  have 
hitherto  prevented  the  more  general  adoption  of  the  bolt  gun, 
although  its  advantages  were  recognized  by  the  Prussians  as 
early  as  1847. 

1.  The  risk  of  premature  discharge  from  striking  an  over- 
sensitive cartridge  in  loading. 

This  was  long  considered  an  insuperable  objection,  but,  as 
will  be  seen,  has  been  overcome  by  very  simple  means. 

2.  The  danger  resulting  from  the  necessity  of  loading  the 
piece  at  a  full  cock. 

This  objection  neglected  the  supreme  advantage  of  the 
rapidity  of  fire  which  results  from  suppressing  a  discontinuous 
motion,*  and  which  is  further  increased  by  the  facihty  with 
which  the  reciprocating  motion  of  the  bolt  adapts  itself  to 
the  demands  of  magazine  arms. 

To  illustrate  the  latest  type  of  this  arm,  the  American 
Lee  system  is  described,  as  it  contains  in  probably  the  best 


*The  word  is  used  as  in  the  drill  book. 


XXVIII. — SMALL    ARMS. 


and  simplest  form  the  elements  of  the  mechanism  required 
for  performing  the  functions  above  named.* 

Lee  System  (as  single  loader)    Figures  1  and  2. 

Descripiion, 

The  receiver,  of  approximately  cylindrical  form,  is  screwed 
to  the  breech  and  receives  the  mechanism.  It  is  bored  out 
and  slotted  to  permit  the  axial  motion  of  the  bolt.  The  slot  is 
widened  to  the  front  to  form  the  well  of  the  receiver,  through 
which  the  operations  of  loading  and  ejection  are  performed. 

The  rectangular  shoulder  at  a  forms  a  support  for  the  locking 
mass,  a\  of  the  bolt  in  firing,  and  the  oblique  edge  at  b  gives  a 
short,  spiral  motion  to  the  bolt  as  the  locking  mass  is  ap- 
proaching or  leaving  its  support. 

The  system  is  mortised  vertically  through  the  well  to  receive 
the  magazine.  As  this  is  a  special  feature  of  the  arm,  its 
consideration  is  deferred  until  the  features  common  to  the 
best  bolt  guns  have  been  discussed. 

The  reciprocating  motion  of  the  bolt  sets  the  whole 
mechanism  in  motion. 

The  /ia7idle  is  placed  in  rear  and  is  curved  downward  so 
that  the  hand  need  not  leave  it  in  firing. 

A  lug  diametrically  opposite  to  the  locking  mass  engages 
with  a  corresponding  recess  in  the  bore  of  the  receiver,  so 


*The  Prussian  Needle  Gun  used  a  combustible  cartridge  case,  the 
fouling  from  which  tended  to  obstruct  the  chamber ;  the  joint  was  most 
imperfectly  sealed,  the  flames  escaping  not  only  around  the  end  of  the 
bolt,  but  into  the  channel  traversed  by  the  firing  needle.  The  tactical  ad- 
vantages of  the  arm,  however,  offset  these  very  serious  objections,  so 
that  it  was  retained  unchanged  until  adapted  to  metallic  ammunition 
after  the  war  of  1870. 

Its  opponent  in  this  war,  the  Chassepot,  was  of  similar  construction, 
but  possessed  for  the  end  of  the  bolt  a  gas  check,  from  which  that  of 
Colonel  De  Bange  is  derived. 


XXVIII. — SMALL    ARMS. 


that,  by  making  the  support  symmetrical,  certain  objectionable 
vibrations  of  the  barrel  may  be  avoided. 

The  bolt  contains  an  axial  firing  pin  which  is  surrounded 
by  a  spiral  main  spring  and  secured  to  the  hammer. 

The  bolt  carries  in  front  and  to  the  right  a  hook  shaped 
extractor^  which,  like  the  hammer,  is  so  disposed  as  to  share 
only  in  the  motion  of  translation  which  the  bolt  receives. 
The  extractor  is  retained  by  a  flat  spring  which  serves  also  to 
key  the  system  together. 

Operation. 

To  open  the  piece,  raise  the  handle  so  that  the  locking 
mass  may  lie  in  the  prolongation  of  the  slot,  and  withdraw 
the  bolt. 

The  incipient  rotation  of  the  bolt  is  ingeniously  commuted 
into  one  of  translation  at  each  of  its  ends ;   as  follows  :  — 

In  rear,  a  radial  projection  on  the  bolt  strikes  an  oblique 
surface  on  the  hammer  and  forces  it  back  relatively  to  the 
bolt  until  the  point  of  the  firing  pin  is  retracted,  or  withdrawn 
behind  the  plane  surface  in  contact  with  the  cartridge.  To 
avoid  premature  explosion  the  point  of  the  firing  pin  is  kept 
back  until  the  desired  moment  of  discharge. 

In  front,  the  spiral  motion  due  to  the  surface,  b,  forces  the 
bolt  slowly  back  from  the  barrel  so  that  power  is  obtained  to 
start  the  fired  cartridge  case  from  its  seat.  This  slow  and 
therefore  powerful  motion  of  extractiofi  is  commonly  used. 
A  rapid  motion  might  cut  through  the  cartridge  rim  and  dis- 
able the  rifle. 

As  the  bolt  is  withdrawn,  the  extracted  case  foflows  until  it 
passes  from  the  chamber.  The  rim  then  strikes  the  ejector 
stud,  a  projection  on  the  bore  of  the  receiver  opposite  to  the 
path  of  the  extractor.  The  case  is  thereby  rapidly  revolved 
about  the  hook  and  ejected,  or  thrown  clear  of  the  gun. 

A  cartridge  may  then  be  dropped  into  the  well,  the  bottom 


XXVltl. — SMALL   ARMS. 


of  which  is  nearly  continuous  with  the  lower  element  of  the 
chamber.  A  reversal  of  the  motions  forces  the  cartridge  into 
,<lace  and  locks  the  breech. 

The  surface,  ^,  now  serves  to  prevent  the  shock  referred  to 
on  page  6,  and  also  to  make  the  motion  of  the  hand  con- 
tinuous. 

In  the  final  motion  of  closing,  the  mainspring  is  fully  com 
pressed,  or  the  piece  is  cocked,  by  the  interposition  of  the 
sear,   the  nose  of  which  arrests   the  forward  motion  of  the 
hammer  while  the  bolt  moves  on. 

The  U  shaped  sear  spring  acts  against  the  trigger  through 
the  sear;  so,  that  when  the  trigger  is  drawn,  the  sear  spring 
is  compressed,  the  sear  is  lowered  -and  the  hammer  allowed 
to  fall. 

Remarks. 

Opening^  closing  and  loading.  These  operations  are  safely 
and  rapidly  performed. 

Locking,  The  method  is  of  great  simplicity  and  affords  a 
sohd  support.  Jointed  surfaces,  however  well  made,  permit 
an  objectionable  displacement  under  the  stress  of  firing. 

Firing.  The  coiled  spring  is  admirably  adapted  to  the 
purpose,  since,  owing  to  its  developed  length,  the  stress  on 
any  of  its  spires  is  slight ;  and,  owing  to  its  position  on  the 
pin,  it  will  continue  to  work,  even  if  broken. 

Extraction  and  ejection.  These  are  readily  performed, 
Vven  with  inferior  ammunition. 

Assembling.  The  parts  are  few  in  number,  strong  and  simple. 
They  are  arranged  so  as  to  avoid  the  effects  of  rust  and  dust, 
and  are  so  connected  as  to  be  readily  dismounted  for  cleaning 
without  the  use  of  special  tools. 

MAGAZINE  ARMS. 

If  by  any  means  a  succession  of  cartridges  can  be  auto- 
matically placed  in  front  of  the  bolt  as  it  is  closing,  a  mag- 
azine gun  will  result. 


10  JCXVIIl.— SMALt    ARM§ 


This  has  been  accomplished  in  many  ways  which  may  be 
classified.  1st.  According  as  the  niagazmes  are  tubular,  or 
box  shaped,  2nd.  According  as  they  are  permanently  fixed 
to  the  gun,  or  are  detachable.  The  tubular  magazines  are 
always  fixed. 

TUBULAR    MAGAZINES. 

These  may  lie  either,  1st,  in  front,  as  beneath  the  barrel, 
or  2nd,  in  the  cylindrical  volume  lorming  the  small  of  the 
stock  and  its  prolongation  in  rear. 

A  spiral  spring  forces  the  contents  of  the  tube  toward  the 
receiver,  and  a  valve  regulates  their  entrance. 

In  the  first  class  a  carrier,  operated  by  the  withdrawal  of 
the  bolt,  raises  the  cartridges  successively  from  the  mouth  of 
the  tube  to  the  mouth  of  the  chamber.  See  figure  3  for  one 
form  of  carrier. 

The  operation  is  that  of  the  bell  crank.  Chapter  XXIX, 
figure  7^ 

Advantages. 
This  form  of  magazine,  used  in  the  French  Lebel  Rifle, 
adapts  itself  to  the  profile  of  the  gun.  When  in  front,  the 
capacity  is  large  for  cartridges  which  are  short  and  thick,  and 
a  simple  trap  door  on  the  side  permits  the  magazine  to  be 
filled  without  opening  the  breech,  /.  e.,  luithout  unloading  the 
gun. 

Disadvafitages. 

The  cartridges  lie  end  to  end,  and  in  firing  are  exposed  to 
shocks  which  may  explode  them  or  deform  them  sufficiently 
to  interfere  with  the  regularity  of  the  feed. 

The  feed  acts  in  the  direction  of  the  longest  dimension  of 
the  cartridge. 

For  the  front  magazine  the  weight  is  not  well  distributed ; 
and  for  that  in  the  butt  the  capacity  is  smal^,  and  the  filling 


XXVIII. — SMALL   ARMS.  11 

of  the  magazine  is  complicated  with   the  unloading  of  the 
gun. 

The  operation  of  filling  is  slow,  since  the  cartridges  are 
passed  in  singly ;  and,  since  nothing  external  indicates  the 
state  of  the  supply,  the  control  of  the  fire  by  the  soldier,  and 
of  the  soldier  by  the  ofticer  is  impaired. 

The  "Cut-off." 

By  a  device  which  may  limit  the  withdrawal  of  the  bolt, 
the  magazine  may  be  'Wut-ojf  and  its  contents  reserved  for 
a  suitable  necessity.  The  piece  meanwhile  is  used  as  a  single 
louder. 

Such  attachments  are  fragile  and  in  moments  of  excitement 
are  confusing.  When  tried  under  such  circumstances,  they 
have   been  found  unsuited  to  the  conditions  of  service. 

BOX    MAGAZINES. 

By  placing  the  cartridges  side  by  side  in  a  box,  many  of 
the  objections  urged  against  the  tube  disappear.  The 
principal  point  to  be  decided  relates  to  whether  the  box 
shall  be  detachable  or  fix 

1.  Detachable  Box- 

An  example  of  this  type  is  seen  in  the  Lee  magazine, 
figure  2,  which  consists  of  a  box  of  sheet  steel,  in  which  the 
cartridges  lie  over  the  feed  spring,  N. 

The  box  is  readily  inserted  through  the  mortise  in  the  well 
of  the  receiver  into  the  position  shown. 

The  operation  of  the  bolt  passes  the  cartridges  in  succes- 
sion into  the  chamber,  and  acts  as  a  valve  to  regulate  the 
ascent  of  those  lemainmg  to  be  fired. 

A  number  of  these  magazines  are  carried  by  the  soldier, 
who  IS  expected  to  use  his  arm  as  a  single  loader  until  he 
receives  the  order  to  fix  magazines. 


12  XXVIII. SMALL    ARMS. 

This  facilitates  control  by  the  officer,  but  the  uncertainty 
of  the  soldier  as  to  the  state  of  the  supply  may  lead  him  to 
go  through  the  motions  of  firing  with  an  empty  arm. 

The  principal  objection  to  the  system  applies  to  the  ex- 
cessive weight  and  cost  of  the  box  as  a  package,  if  many 
magazines  are  carried;  and,  if  but  few,  to  the  probabiHty  of 
losing  so  important  a  component  in  the  act  of  replacing  it 
under  fire. 

2.  Fixed  Box. 

I.  A  prominent  arm  of  this  type  is  the  Austrian  Mannlicher 
rifle,  figure  4. 

The  cartridges  are  held  by  their  bases  in  a  sheet  metal 
frame,  the  whole  package  being  bodily  inserted  into  the 
magazine  through  the  well  of  the  receiver,  where  it  is  retained 
by  a  spring  latch,  r,  A  follower^  /,  impelled  by  a  strong 
spring,  ^,  lifts  the  column  so  that  the  top  cartridges  are  suc- 
cessively shoved  into  the  chamber  by  the  bolt.  The  fall  of 
the  empty  case  through  the  bottom  of  the  magazine  warns 
the  soldier  that  the  magazine  is  exhausted. 

In  a  recent  model  the  heads  of  the  cartridges  are  so  held 
by  the  frame  that  they  lie  in  the  same  plane.  With  this 
model  no  special  care  is  needed  in  inserting  the  frame  into 
the  magazine;  while  in  that  shown,  the  obliquity  of  the  frame, 
caused  by  the  step-like  arrangement  of  the  heads,  may  cause 
confusion. 

The  device  for  locking  the  arm  consists  of  a  brace,  b^ 
attached  to  the  bolt.  It  is  forced  downward  in  front  of  a 
shoulder,  t",  in  the  receiver,  by  a  wedge-shaped  projection 
below  an  axial  stem  to  which  the  knob,  k^  is  attached.  By 
simply  pulling  on  the  knob,  the  brace  is  lifted  from  its  seat 
by  the  wedge,  and  the  brace,  knob  and  bolt  slide  out  together. 

This  arrangement  avoids  the  rotation  of  the  bolt  required 
in  the  Lee  and  in  almost  every  other  bolt  gun. 


XXVIII. — SMALL   ARMS.  13 

This  arm  cannot  be  used  as  a  single  loader. 

2\  The  Schulhojf  magazine  rifle,  figure  5,  may  be  used  as 
such  or  as  a  single  loader. 

The  cartridges  are  carried  in  an  annular  box,  beneath  the 
receiver. 

The  axial  shaft,  s,  carries  a  radial  plate,  ox  follower,  f,  that 
ia  turned  m  one  direction  by  the  act  of  opening  the  lid,  /, 
figure  6,  and  m  the  other  direction  by  a  spiral  spring  (not 
shown)  surrounding  the  shatt,  which  is  twisted  in  the  act  of 
opening. 

The  cartridges  may  be  thrown  in  loosely,  or  may  be  loaded 
in  mass  from  the  quick  loader  shown  in  figure  7. 

A  circumferential  slide,  <:,  operated  by  the  thumb  piece  /, 
forms  a  very  simple  cut-off. 

The  strength  and  solidity  of  the  magazine  enables  it  to  be 
slit,  so  that  the  state  of  the  supply  may  be  seen  at  a  glance. 

The  position  of  the  box  enables  it  to  be  filled  without 
unloading  the  arm. 

Quick  Loader. 

A  cheap  quick  loader,  figure  7,  containing  the  supply  of 
cartridges  for  one  magazine  enables  them  to  be  transferred 
to  it  in  mass  when  rapid  recharging  is  required.  For  this 
purpose  the  lower  end  of  the  quick  loader  being  placed  over 
the  mouth  of  the  magazine  the  pressure  of  the  thumb  of  the 
operator  on  top  of  the  column  of  cartridges  forces  them 
down  into  the  magazine  against  the  resistance  of  the 
magazine  spring. 

They  are  retained  by  a  valve  at  the  mouth  of  the  magazine, 
and  the  quick  loader  is  then  thrown  away.     The  valve  serves 
to  retain  successive  cartridges  singly  loaded. 
Form  Proposed. 

The  eventual  preference  of  the  fixed  or  the  detachable 
box  magazine  will  probably  be  largely  determined  by  moral 
considerations. 


14  I  XXVIII. SMALL    ARMS. 

The  dispersed  formations  of  future  wars  will  probably 
require  a  more  extended  exercise  of  discretion  in  the  lower 
grades  than  has  hitherto  been  customary.  The  question 
arises,  how  far  down  will  the  discretionary  control  of  fire 
extend  ? 

It  is  now  proposed  to  attach  the  box  magazine  perma- 
nently to  the  receiver,  and  ordinarily  to  load  the  arm  con- 
tinuously through  the  magazine,  so  that  the  cartridge  last 
inserted  shall  be  the  first  to  be  fired  and  that  the  number 
remaining  shall  be  automatically  held  in  reserve. 

It  is  possible  that  the  time  gained  by  making  the  opera- 
tion of  the  piece  simple  and  invariable,  as  in  the  type  pro- 
posed, may  be  so  utilized  in  the  general  instruction  of  the 
troops  that  it  will  not  be  considered  necessary  to  burden 
them  with  an  inferior  weapon  in  order  to  control  their  fire. 

REQUISITES    OF    A    MAGAZINE    ARM. 

The  preceding  considerations  enable  us  to  name  the  fol- 
lowing necessities : 

1.  The  best  ballistic  conditions  attainable.  These  may 
modify  the  size  and  proportions  of  the  cartridges,  and  so 
affect  the  capacity  of  the  magazine. 

2.  Consecutive  rapidity  of  fire  as  a  single  loader  as  great 
as  that  of  any  other  arm,  and  the  greatest  possible  inter- 
mittent rapidity  when  the  magazine  is  employed. 

3.  The  possibility  of  filling  the  magazine  with  single  car- 
tridges, or  "  in  mass,"  without  unloading  the  piece. 

4.  A  maximum  capacity  which  is  yet  to  be  determined 
by  experience.  It  will  probably  be  about  5  shots  in  the 
magazine. 

5.  A  ready  view  of  the  state  of  the  supply. 

6.  The  most  simple  construction  compatible  with  the 
maximum  efficiency  under  the  conditions  of  service. 

Beyond  a  certain  point  objections  to  complexity  become 


Xxviii. — Small  arms.  18 


pedantic,  since  experience  shows  that  the  instinct  of  self- 
preservation  may  be  counted  on  for  the  care  necessary  to 
maintain  an  efficient  arm. 

THE  SPRINGFIELD  RIFLE. 

History. 

This  arm,  although  originally  intended  as  a  means  of 
utilizing  the  large  supply  of  muzzle  loading  muskets  left  by 
the  Civil  War,  has  acquired  a  standing  which,  in  1886, 
caused  its  preference  by  73  per  cent  of  the  officers  to  whom 
were  submitted,  for  comparative  trial  in  service,  three  of  the 
best  magazine  arms. 

Apart  from  the  excellence  of  its  manufacture  and  the  ease 
with  which  it  may  be  operated  with  but  one  hand,  this  pre- 
ference may  be  attributed  to  the  independent  action  of  a 
form  of  lock,  the  outgrowth  of  centuries  of  experience ;  and 
the  perfection  of  the  apparatus  for  extraction  and  ejection. 

The  design  of  the  cam  latch  and  of  the  firing  pin  are 
exposed  to  criticism. 

As  a  reserve  supply  of  this  arm  is  likely  to  be  retained  for 
many  years  after  the  adoption  of  a  magazine  gun,  a  few  of 
its  principles  are  described.  The  nomenclature  is  supposed 
to  be  known. 

Operation.    Figure  8. 

Locking. 

When  the  piece  is  fired  the  tendency  of  the  block  to  swing 
upward  out  of  the  receiver,  A^  is  corrected  by  the  loose  fit 
of  the  hinge  pin,  E^  in  its  hole.  The  block,  therefore,  sHdes 
bodily  to  the~rear  until  stopped  by  the  interposition  of  the 
body  of  the  cam  latch  F,  between  the  block  and  the  breech 
screw,  C.  The  journals  of  the  cam  latch  are  loose  in  their 
bearings  so  that  they  may  be  free  from  strain. 

The  centre  of  pressure  on  the  breech  screw  is  brought 


16  XXVIII. — SMALL   ARMS. 

as  nearly  as  possible  in  the  prolongation  of  the  axis  of 
the  bore  so  as  to  diminish  the  tangential  component  of  the 
pressure,  which  tends  to  revolve  the  cam  latch  and  tlirow 
open  the  block.  This  is  imperfectly  resisted  by  the  friction 
developed  by  the  normal  pressure  between  the  surfaces  in 
contact,  and  also  by  the  combined  action  of  the  thumb  piece 
and  the  hammer,  the  functions  of  which  are  thereby  perverted. 

Extraction. 
The  power  needed  for  extraction  results  from  the  compound 
lever  formed  by  the  breech  block  and  the  extractor,  J, 

Ejection. 

In  opening  the  block  the  revolution  of  the  extractor  com- 
presses the  coiled  ejector  spring,  K,  until  the  action  line  of 
this  spring  passes  from  above  the  axis  of  rotation  to  below  it. 

The  expansion  of  the  spring  then  rapidly  revolves  the  ex- 
tractor. This  impels  the  cartridge  case  against  the  ejector 
stud  Z,  which  deflects  it  upward  and  throws  it  clear  of  the  gun. 

Firing  Mechanism. 

The  lock,  figures  9,  10,  11,  consists  of  the  lock  plate,  to 
which  the  parts  are  attached  and  by  which  the  mechanism  is 
secured  to  the  stock  by  the  side  screws. 

The  hammer,  A^  outside  the  lock  plate,  and  the  tumbler,  B^ 
inside  of  it  form  mechanically  but  one  piece,  the  arrangement 
adopted  being  required  for  the  protection  of  mechanism  from 
dirt. 

The  tumbler,  B,  is  connected  with  the  mainspring  by  a 
swivel,  y,  so  disposed  that  the  resistance  to  cocking  the  piece 
shall  be  nearly  constant.  This  is  accomplished  by  the  varia- 
tion in  the  lever  arm  of  the  mainspring ;  as  the  resistance  of 
the  mainspring  due  to  its  compression  increases,  the  action 
line  of  the  resistance  passes  nearer  to  the  axis  of  the  tumbler, 


kXVlIt. — SMALL  ARMS.  17 

while  the  lever  arm  of  the  power,  the  thumb,  is  constant. 
The  tumbler  is  thrice  notched  to  receive  the  nose  of  the  sear, 
E.  This,  under  the  action  of  the  sear  spring,  G^  maintains 
the  hammer  at  the  distances  from  the  head  of  the  firing  pin 
required  for  convenience  of  transportation,  safety  of  loading, 
and  certainty  of  fire,  respectively. 

The  bridle,  C,  holds  the  parts  together. 

The  oblique  blow  of  the  firing  pin  is  objectionable.  Chap- 
ter XXVII,  page  5. 

RECENT  DEVELOPMENT  OF  SMALL  ARMS. 

PHYSICAL   CONSTANTS. 

Owing  to  the  mechanical  improvements  in  the  construction 
of  arms  and  ammunition  the  ballistic  development  of  the  small 
arm  is  now  limited  by  the  soldier's  endurance  of  its  recoil. 
Similarly  its  tactical  employment  is  limited  by  his  ability  to 
transport  the  burden  of  its  ammunition  ;  for  the  maintenance 
of  the  rapid  fire  of  the  extended  lines  now  rendered  possible 
is  a  problem  which  increases  in  difficulty  as  the  fire  increases 
in  rapidity  and  range. 

L  Recoil. 

These  constants  are  influenced  by  racial  peculiarities,  and 
may  be  considerably  modified  by  training  ;  but  the  proper 
training  of  large  armies  in  the  endurance  of  recoil  implies  so 
great  a  cost,  that  the  present  tendency  is  to  render  the  recoil 
supportable  by  inexperienced  troops,  so  that  the  accuracy  of 
their  fire  may  not  be  impaired  by  their  apprehension  of  its 
effects.* 


*Tlie  effect  of  racial  peculiarities,  and  incidentally  of  training,  is  shown 
by  the  following  data  which  relate  to  arms  of  caliber  about  0.45  in. 

In  the  relatively  small  armies  of  Great  Britain  and  the  U.  S.  the  energy 
of  recoil  IS  about  14  ft.  pounds. 

The  low  average  stature  of  the  French  fixes  a  limit  of  about  11  ft. 


18  XXVIII. — SMALL   ARMS. 

2.  Burden. 

Training  in  weight-carrying  is  not  expensive,  and  its  im- 
portance is  becoming  recognized  by  the  frequency  with  which 
practice  marches  are  made.  As  in  the  artillery  service 
Chapter  XXIV,  page  2,  a  judicious  distribution  of  the  bur- 
den between  the  arm  and  its  ammunition  depends  greatly 
upon  the  former's  recoil. 

MODIFICATIONS    OF    THE    RECOIL. 

The  recoil  may  be  reduced  by  modifying  the  arm  or  the 
ammunition. 

1.  Modifications  in  the  Arm. 

If  the  ballistic  conditions  are  kept  constant,  the  weight  of 
the  arm  may  be  reduced,  and  a  greater  number  of  cartridges 
be  carried,  by : — 
,  1.  The  use  of  an  elastic  cushion  attached  either  to  the  gun 
or  to  the  clothing. 

These  plans  are  found  impracticable. 

2.  Increasing  the  mass  of  the  gun  in  firing  by  adding  to  it 
that  of  a  portion  of  the  ammunition,  as  in  magazine  guns. 

The  correction  is  variable  and  sometimes  injurious  to 
accuracy. 

3.  Storing  up  the  energy  of  recoil  as  by  the  compression  of 
a  spring,  which,  by  its  resihence  may  operate  the  piece. 


pounds.  But  in  Germany,  although  the  ballistic  conditions  are  nearly 
identical  with  the  French,  the  desire  for  durability  has  developed  the 
heaviest  small  arm  known.  Notwithstanding  the  strength  of  the  Ger- 
mans the  recoil  is  only  10  ft.  pounds. 

In  Italy,  as  in  our  service  during  the  Civil  War,  about  7  ft.  pounds  is 
allowed. 

This  IS  the  limit  reached  by  the  present  reduction  in  caliber.  The  re- 
turn to  the  former  standard,  page  23,  is  significant  of  its  practical  con- 
stancy. 


XXVIII. — SMALL   ARMS.  19 

This  has  been  tried,  but  so  far  without  success,  owing  to  the 
complicated  nature  of  the  mechanism  required. 

4.  The  pressure  due  to  the  recoil  may  be  distributed  over 
an  increased  area  of  the  person  by  the  proper  use  of  the  gun 
sling.  By  lying  down  to  fire,  the  path  of  the  recoil  is 
shortened  and  the  pressure  on  the  body  increased. 

General  consent  seems  to  have  established  the  weight  of 
the  rifle  at  between  8.5  and  9.5  pounds. 

2.  Modifications  in  the  Ammunition. 

1.   Caliber  and  Recoil  Constant, 

The  advantages  of  any  particular  cahber  being  general, 
that  of  all  military  rifles  at  any  epoch  is  approximately  con- 
stant.    It  has  recently  been  about  0.45  inch.     See  figure  12. 

When  the  caliber  and  the  weight  of  the  arm  are  constant, 

the  recoil  can  be  reduced  only  at  the  expense  of  the  ballistic 

properties  of  the  arm.     But  these  being  maintained  at  the 

highest   value    consistent  with  the  recoil  endurable   in  any 

i  7n  v  V 
particular  case,  the  Equation  M  E  ■=.  C  ^  - — - — -  shows 

that  modifications  in  the  ammunition  must  be  confined  to 
factoring  the  momentum  of  the  projectile.  The  following 
considerations  illustrate  the  effect  of  variations  in  m  and  z', 
their  product  in  any  one  case  being  constant. 

a.  If  we  increase  w  at  the  expense  of  z/,  we  lose  in  danger- 
ous space  at  short  and  decisive  ranges  but  conversely  at  long 
distances.     Chapter  XX,  page  40. 

b.  During  the  wars  of  1870  and  1877  it  was  found  advis- 
able to  deliver  at  extreme  ranges  an  almost  vertical  fire 
against  masses  of  troops. 

It  has  since  been  found  that  the  extreme  range  increases 
more  rapidly  with  the  sectional  density  of  the  bullet  than 
with  its  initial  velocity.     The  present  U.  S.  bullet  was  accord- 


20  XXVIII. — SMALL   ARMS. 

ingly  increased  in  weight  from  405  to  500  grains,  and  an 
extreme  range  of  two  miles  was  attained. 

c.  It  is  found  that  the  accuracy  of  fire  at  moderate  known 
distances  is  incompatible  with  tlie  high  velocities  required  in 
actual  service.  This  is  probably  due  to  the  vibration  of  the 
barrel.     Page  4. 

Conclusion. 

Owing  to  the  impossibility  of  simultaneously  satisfying  the 
requirements  of  the  different  ranges,  it  is  considered  that 
efficiency  at  long  ranges  should  be  sought  by  the  use  of  special 
means,  such  as  machine  guns  firing  heavy  projectiles.  For 
small  arms  it  is  considered  that  accuracy  should  become  sub- 
ordmate  to  flatness  of  trajectory  for  ranges  exceeding  600 
yards,  at  which  individuals  cease  to  be  distinguished  by  the 
unaided  eye ;  and  that  the  trajectory  should  be  so  flat  that 
but  one  height  of  the  rear  sight  would  be  required  within  that 
distance,  and  the  smallest  number  of  changes  beyond  it. 

Differences  of  elevation  within  the  limits  of  graduation 
would  be  adjusted  by  varying  the  coarseness  of  the  front 
sight.     Chapter  XXX,  page  2. 

2.  Caliber  Variable. 
These  conditions  can  be  attained,  and  the  number  of  cart- 
ridges in  a  given  burden  increased,  by  reducing  the  caliber. 
Under  the  conditions  named  on  page  2,  the  limit  of  reduc- 
tion has  been  fixed  by  the  difficulties  of  manufacture  and  by 
those  relating  to  the  cleaning  of  the  bore. 

Small  Caliber  Rifle. 

The  following  general  principles  govern  the  changes  in 
ammunition  resulting  from  the  reduction  in  caliber.  For 
simpHcity  of  treatment  we  will  first  assume  the  muzzle  velocity 
unchanged  from  the  larger  caliber. 

Bullet,     The  sectional  density,  and  therefore  the  length  of 


XXVIII. — SMALL   ARMS.  21 


the  bullet,  has  remained  approximately  constant ;  since,  as 
shown  in  Chapter  XVI,  page  4,  an  increase  in  the  sectional 
density  would  increase  the  value  of  /„,  unless  the  muzzle 
velocity  were  reduced. 

The  strength  of  the  barrel  is  not  materially  greater  than 
that  of  the  caliber  0.45,  and,  owing  to  the  reduction  in  the 
area  corresponding  to  the  bottom  of  the  bore,  the  increase 
in  the  strength  of  the  fermeture  is  only  relative ;  therefore, 
the  maximum  value  of  p^  formerly  allowed  cannot  be  greatly 
exceeded. 

The  sectional  density  being  constant,  the  reduction  in 
caliber  reduces  the  mass  of  the  bullet,  and  therefore,  although 
the  ballistic  properties  of  the  arm  (being  dependent  only 
upon  the  sectional  density  or  C,  Chapter  XX,  and  the  muzzle 
velocity)  would  not  be  affected,  the  recoil  would  be  reduced 

(m'  \  "^ 
— ).     With  the  weights  of  bullet  given  in  the 

following  table,  this  would  reduce  the  recoil  from  about  14 
foot-pounds  to  about  3  foot-pounds. 

Powder,  This  reduction  being  excessive,  the  normal 
endurance  of  the  soldier  against  recoil  is  utilized  by  increas- 
ing the  weight  of  the  charge,  and  therefore  the  muzzle 
velocity. 

The  baUistic  properties  of  the  arm  are  therefore  improved, 
figure  12,  but  the  internal  pressure*  would  be  excessive  unless 


*  If  in  Equation  (D),  Chapter  XII,  we  place  K^a^  /\=z  C,  and  repre- 

IV  ,  .  w 

sent    by    (J  =  -jj  the  sectional  density  of  the  projectile,  and  by  «  =  — 

the  ratio  between  the  weight  of  the  powder  and  that  of  the  projectile,  we 
have,  after  reduction. 

But  if,  as  in  the  case  considered,  6  is  constant,  /„  will  vary  with  nj^. 

From  this  it  follows  that  if  the  same  charge  of  the  same  kind  of  powder 
were  used  in  the  Hebler  rifle  as  in  the  Springfield,  the  pressure  would  be 
nearly  doubled. 


22  XXVIII. — SMALL   ARMS. 


the  powder  were  made  specially  progressive.     The  value  of 

J  for  the  cartridge  shown  in  figure  14  is  11.43.     See  Table  I, 

Chapter  XII. 

In  spite  of  these  precautions  the  main  difficulty  in  the  new 
small  caliber  high-powered  guns  is  due  to  the  excessive  pres- 
sures developed. 

Powder. 

The  principal  difficulties  found  in  realizing  the  advantages 
of  a  reduction  in  caliber  exist  in  the  powder. 

It  was  thought  by  Professor  Hebler,  of  Germany,  to  whom 
much  of  the  credit  of  the  proposed  change  is  due,  that  these 
difficulties  could  be  overcome  by  compressing  the  powder  as 
in  a  rocket,  in  a  cartridge  case  like  the  Morse.     Figs.  13,  14. 

The  objections  to  this  method  noted,  Chapters  XII,  page 

21 ;   XVI,  page  45,  and  the  large  volume  of  smoke  resulting 

from  rapid  fire,  cause  many  to  prefer  a  high  explosive,  such 

as  described,  Chapter  XIV,  page  15  ;  in  spite  of  its  recognized 

objections.     The   complete  solution  of  the  problem  is   still 

deferred. 

Projectile, 

The  projectile  proposed  is  distinguished  by  its  penetration, 
its  cleanliness  as  regards  the  bore,  and  the  nature  of  the 
wounds  which  it  inflicts,  page  2.  When  they  are  flesh  wounds 
they  are  punctured  rather  than  lacerated;  but  when  they 
involve  the  bones  these  are  shattered. 

Cartridge  Case. 

In  order  to  avoid  the  increase  in  the  length  and  weight 
of  the  breech  mechanism,  resulting  from  the  relative  increase 
in  the  length  of  the  cartridge  case,  this  is  made  bottle-shaped, 
as  in  figure  14. 

This  unfits  it  for  reloading  with  compressed  powder,  unless 
the  Morse  cartridge  be  used  ;  the  latter  has  been  found  too 
delicate  to  endure  reloading  by  troops. 


XXVIII. — SMALL  ARMS.  SS 

In  some  cases  the  volume  of  the  magazine  has  been 
diminished  by  eliminating  the  rim  and  replacing  it  by  a  V 
shaped  groove,  in  which  the  hook  of  the  extractor  may 
engage,  figure  16.  In  order  to  faciUtate  reloading  with  per- 
forated cyhnders  of  powder,  previously  compressed,  such  as 
c,  the  cavity  is  cylindrical ;  the  reduction  in  diameter  being 
made  by  a  brass  ring,  r.  The  blow  of  the  hammer  is  sup- 
ported by  XhQ  front  of  the  cartridge  case. 

Comparison. 

The  following  table  illustrates  the  advantages  of  the 
reduced  cahber,  since  it  compares  the  present  Springfield 
rifle,  which  is  one  of  the  best  of  the  arms  recently  used, 
with  the  Hebler,  which  is  a  fair  type  of  the  arms  proposed  : 


Springfleld. 

Hebler. 

Caliber,  inches 

0.450 

0.296 

Bullet,  wt.  grains, 

500 

225 

Powder,  wt.  grains. 

70 

83 

Sectional  density, 

0.353 

0.367 

Spherical  density. 

3.6 

5.6 

Twist  in  inches, 

22 

4.58 

Twist  in  calibers,  ratio  about, 

3 

1 

Initial  velocity,  f.  s., 

1280 

1942 

Cartridges,  ratio  of  weights, 

100 

85. 

Arm,  weights  pounds. 

9.3 

9.9 

Maximum  dangerous  space,  yds.. 

880 

440 

Accuracy  at  440  yds.,  ratio 

1 

3 

Muzzle  energy,  foot-pounds. 

1818 

1882 

Recoil  energy,  foot-pounds. 

13.95 

6.11 

REVOLVERS, 

As  a  military  weapon  the  revolver  is  useful  principally  in 
enabling  a  horseman  to  use  but  one  hand  in  delivering  a 
rapid  fire.     In  closed  masses  its  employment  is  dangerous, 


24  XXVlll. — SMALL  ARMS. 

since  it  is  difficult  to  fire  to  the  front  without  striking  the 
horse  or  the  leading  files,  and  the  shortness  of.  the  piece 
leads  to  accidents  to  those  alongside. 

It  is  therefore  considered  generally  an  inferior  arm,  and  one 
to  be  used  only  for  personal  defence  and  in  maintaining  dis- 
cipline upon  the  field.  Its  ballistic  properties  need  not  be 
greater  than  necessary  to  stop  a  man  at  50  or  60  yards. 

The  revolver  is  one  of  the  oldest  forms  of  magazine  arms. 
Its  present  perfection  is  due  to  the  invention  of  Col.  Colt  of 
Hartford,  who  combined  the  cocking  of  the  hammer  with 
the  revolution  of  the  cylinder. 

Owing  to  the  considerable  moment  of  inertia  of  the  loaded 
cylinder,  this  tends  when  rapidly  revolved  to  pass  the  position 
in  which  the  axis  of  the  chamber  next  to  be  fired  coincides 
with  that  of  the  barrel.  This  is  the  principal  difficulty  found 
in  the  construction  of  these  arms. 

To  facihtate  their  operation,  revolvers  are  sometimes  made. 
self'Cockifig,  the  action  of  the  trigger  causing  all  the  motions 
to  be  performed.  For  greater  continuous  rapidity  of  fire,  in 
which  these  arms,  like  many  magazine  rifles,  are  deficient, 
the  cartridges  may  be  simultaneously  extracted  by  sliding  or 
swinging  the  barrel  and  cylinder  away  from  the  breech.  The 
chambers  may  then  be  simultaneously  reloaded  by  using 
ammunition  packed  in  clusters. 

The  complexity  of  these  refinements  and  the  limited  scope 
of  the  revolver  generally  cause  simpler  patterns  to  be  pre- 
ferred. 

MANUPACTURE   OF    SMALL   ARMS. 

Where  Made. 

The  service  rifle  and  carbine  are  made  by  the  Ordnance 
Department  at  the  National  Armory.  Pistols  and  such  other 
special  arms  as  may  from  time  to  time  be  needed  are  bought 
from  private  estabUshments. 


XXVIII. — SMALL  ARMS.  25 

How  Made. 

Efficiency  in  service  and  ultimate  economy  in  manufacture 
require  that  the  similar  parts  of  arms  of  the  same  model  shall 
be  interchangeable.  This  is  secured  by  the  principle  of 
gauging,  noted  in  Chapters  IV  and  XVII. 

Gauging. 

The  general  design  of  a  gun  having  been  perfected,  an 
exact  working  model  is  carefully  prepared.  The  component 
parts  are  so  formed  as  to  be  as  far  as  possible  adapted  to  the 
operation  of  the  varieties  of  the  lathe.  Chapter  XVII, 
page  13. 

Each  of  the  components  is  then  examined  with  reference 
to  its  gauging  points.  These  are  the  surfaces  between  which 
the  most  exact  relations  are  required. 

For  surfaces  of  revolution  like  the  barrel,  or  parts  intended 
to  revolve  like  the  Springfield  breech  block  and  the  tumbler, 
the  gauging  points  are  established  with  reference  to  the  axis 
of  rotation. 

For  pieces  subject  to  compression,  like  the  bolt  of  the  Lee 
rifle,  the  greatest  pains  would  be  taken  with  the  distance  from 
the  rear  face  of  the  locking  mass,  a',  to  the  front  face  of  the 
bolt ;  and,  in  the  receiver,  with  the  distance  from  the  shoulder, 
a,  to  the  plane  containing  the  mouth  of  the  chamber,  since 
the  difference  of  these  distance  must  be  kept  invariable  in 
order  to  insure  the  proper  working  of  the  ammunition. 

While  the  first  of  these  is  readily  gauged,  the  second  in- 
volves the  relations  between  the  barrel  and  the  receiver ; 
each  of  which  must  be  similarly  watched  with  reference  to 
their  abutting  surfaces. 

When  the  number  of  such  surfaces  is  considerable,  as  in 
the  Springfield  mechanism,  the  sum  of  their  possible  errors 
requires  the  closest  gauging  of  each  link  of  the  chain  of  parts. 

Many   forms  of  gauges   are   employed.      They   may   be 


26  XXVIII. — SMALL   ARMS. 

classified  like  patterns  as  positive  or  negative  gauges,  the 
latter  being  sometimes  simple  notches,  and  sometimes  mat- 
rices so  formed  as  to  contain  exactly  pieces  of  an  irregular 
shape. 

To  retard  their  wear,  the  working  surfaces  of  gauges  are 
made  of  hardened  steel ;  and,  as  steel  tends  in  hardening 
to  change  its  form,  these  surfaces  are  finished  in  the  hardened 
state. 

The  number  of  gauges  required  not  only  for  the  finished 
parts  but  for  the  intermediate  stages  demand  that,  before  the 
first  arm  of  a  series  be  produced,  many  thousand  dollars  shall 
be  expended  in  preparation. 

When  tlie  gauges  and  the  corresponding  tools  and  fixtures 
are  made,  the  work  goes  on  rapidly  ;  for  the  functions  of  each 
workman  are  independent,  and  no  time  is  wasted  in  fitting 
the  product  of  different  hands. 

In  illustration:  The  model  may  cost  $600  —  the  first  hun- 
dred guns  made  from  the  gauges  $100  each,  and  the  first  ten 
thousand,  all  equal  in  quality  to  the  model,  $15  each. 

The  sense  of  feeling  is  so  much  more  acute  than  that  of 
sight,  that  by  the  use  of  guages  differences  far  within  the 
limits  of  ordinary  measurement  may  be  detected.  The  thou- 
sandth part  of  an  inch  is  the  customary  unit,  and  this  may 
be  subdivided  practically  according  to  the  requirements  of 
the  work. 

The  system  more  than  anything  else  promotes  the  "division 
of  labor,"  upon  which  industrial  prosperity  depends  ;  and,  by 
substituting  an  absolute  for  a  discretionary  standard,  it  edu- 
cates in  a  remarkable  manner  the  workman  upon  whose  skill 
the  value  of  the  product  is  practically  based. 

OPERATIONS    OF    MANUFACTURE, 

Barrels. 

The  principal  operations  are  rolling,  boring,  turning, 
straightening  and  rifling.     The  rolling  is  done  as  previously 


XXVIII. — SMALL   ARMS.  27 

described,  Chapter  XV,  page  44.  While  hot  the  rough  ends 
of  the  tube  are  sawed  off  and  it  is  straightened  under  a  drop 
hammer,  after  which  it  is  annealed  by  the  residual  heat. 
When  cold  the  hard  scale  is  removed  by  pickling  in  diluted 
acid. 

In  the  preliminary  borings  the  revolving  auger  is  drawn 
through  the  barrel  instead  of  being  pushed,  so  as  to  keep  the 
hole  straight.*  The  bore  is  then  enlarged  by  rapidly  re- 
volving reamers  whose  cross  sections  are  square. 

In  turnhig  the  slide  rest  is  guided  by  a  template  so  as  to 
produce  a  conical  surface,  and  the  barrel  is  kept  from 
springing  by  the  back  rest. 

Straightenifig  is  performed  by  light  blows  of  the  hand 
hammer  appHed  at  points  which  are  indicated  by  the  shadow 
of  a  straight  edge  reflected  from  the  walls  of  the  bore.  This 
operation  requires  a  peculiar  knack  which  very  few  can 
acquire. 

In  order  to  secure  uniformity  in  the  rifling^  a  number  of 
cutters  equal  to  that  of  the  grooves  is  provided  and  these 
are  transferred  automatically  between  adjoining  grooves  at 
the  end  of  each  stroke  of  the  axial  rifling  rod. 

This  rod  receives  a  combined  motion  of  translation  and 
rotation,  by  which,  as  in  rifled  cannon,  the  spiral  motion  is 
produced. 

While  in  an  intermediate  stage,  the  barrel  is  proved  by  fir- 
ing a  very  large  charge  of  both  powder  and  lead. 

The  final  proof  of  the  efficiency  of  the  mechanism  and 
of  the  accuracy  of  the  arm  is  made  with  service  ammunition. 

MANUFACTURE  OF  THE  MINOR  PARTS.  » 

The    form  is  defined  roughly   by   Gorging   between   dies. 


*The  adoption  of  the  0.30  caliber  will  increase  the  difficulty  of  boring 
since  the  barrel  may  require  to  be  rolled  solid  and  bored  under 
compression. 


28  XXVIII. — SMALL   ARMS. 

The  slow  operation  of  a  very  powerful  press  permits  many 
parts  to  be  reduced  to  nearly  their  finished  dimensions 
when  cold. 

The  principles  of  milling,  Chapter  XVII,  are  used  when- 
ever practicable.  The  most  complicated  arms  have  thus 
been  made  without  requiring  the  use  of  the  file. 

The  most  interesting  operations  are  those  required  to  pro- 
duce irregular  forms. 

Profiling. 

The  profiler  is  a  sort  of  milling  machine  in  which  relative 
motion  in  three  coordinate  directions  can  be  produced  between 
the  revolving  mill  and  the  work.  To  limit  the  relative  dis- 
placements the  following  arrangement  is  provided.  See 
figure  17. 

To  a  table  moving  in  a  horizontal  plane  the  work,  W,  is 
clamped  at  a  fixed  distance  from  a  hardened  steel  model,  M, 
of  the  finished  part. 

At  the  same  distance  from  the  mill,  m,  and  with  its  axis 
vertical,  is  a  blank  pin,  /,  of  corresponding  dimensions.  We 
thus  have  two  pairs  of  parts ;  one  pair  consistmg  of  the 
model  and  the  work  and  the  other  of  the  pin  and  the  mill, 
with  relative  motion  between  the  pairs.  When  the  mill  begins 
to  cut  it  is  necessary  only  to  cause  the  pin  to  follow  the  pro- 
file of  the  model  in  order  to  reproduce  it  in  the  work. 

The  intricate  l^ed  or  matrix  of  the  lock  is  thus  formed  with 
the  greatest  accuracy  in  about  one  mmute. 

Eccentric  Turning. 

This  operation  was  devised  by  Thomas  Blanchard,  an  em- 
ployee of  the  National  Armory,  for  the  purpose  of  forming 
the  gun  stock.  It  has  been  applied  to  many  other  useful 
purposes,  as  in  the  manufacture  of  shoe  lasts,  spokes,  and 
even  of  statuary.       Its  principle  is  as  follows:  See  figure  18. 

In  ordinary  turning  the  cutter  does  not  sensibly  change  its 


XXVIII. — SMALL   ARMS.  29 

distance  from  the  axis  during  one  revolution  of  the  work  and 
therefore  leaves  behind  it  a  partically  concentric  surface. 

But  in  eccentric  turning  the  cutter,  C,  which  revolves  after 
the  manner  of  a  mill  about  an  independent  axis  parallel  to  that 
of  the  work,  is  caused  to  oscillate  slowly  in  a  plane  normal 
to  the  axis  of  rotation  during  each  revolution  of  the  work,  JV. 
This  oscillation  is  produced  by  an  iron  model,  J/,  revolving 
with  and  parallel  to  the  work  and  resting  against  a  blank 
wheel,  B,  attached  to  the  oscillating  frame  which  supports 
the  cutter. 

In  concentric  turning  the  cutting  speed  is  due  to  the  tan- 
gential velocity  of  the  work,  and  in  eccentric  turning  the 
high  speed  required  in  wood  working  is  due  to  that  of  the 
cutter.  The  motion  of  translation  is  similarly  performed  in 
both  cases. 

The  cutting  edges  are  placed  at  progressively  increasing 
radial  distances,  so  as  to  cut  to  different  depths  during  each 
revolution  of  the  cutter.  This  principle  is  frequently  applied 
in  revolving  tools. 

The  developed  length  of  the  cuts  required  to  turn  a  gun- 
stock  is  13  miles ;  the  operation  takes  about  8  minutes. 

Blacking  and  Browning. 

To  protect  the  parts  from  rust  and  to  prevent  them  from 
flashing  in  the  sun,  small  pieces  are  blackened  by  heating 
them  until  they  will  ignite  the  oil  with  which  they  are  covered. 

The  outside  of  the  barrel  is  oxidized  by  coating  it  with  a 
dilute  acid  mixture  and  exposing  it  in  a  warm,  damp  place. 
The  loose  coating  of  red  oxide  having  been  brushed  off,  a 
permanent  layer  of  black  rust  remains.  Some  parts  are 
rapidly  oxidized  by  immersing  them  in  fused  nitre. 


XXIX. — CANNON    WITHOUT    RECOIL. 


CHAPTER  XXIX. 

CANNON  WITHOUT  RECOIL. 

The  advantages  of  rapid  fire  from  cannon  would  be 
neutralized  by  the  time  required  to  readjust  the  aim,  were 
it  not  that  means  have  been  found  to  so  control  the  recoil 
that  the  piece  may  return,  between  shots,  to  its  original 
position  and  direction.  Such  systems  may  be  said  to  be 
practically  without  recoil. 

They  may  be  divided  into  two  general  classes.  1st.  Those 
in  which  the  mass  of  the  system  is  so  great  in  proportion  to 
the  momentum  of  the  projectile  that  the  velocity  of  recoil 
may  be  neglected.  2nd.  Those  in  which  so  much  of  the 
energy  of  recoil  of  the  piece  is  absorbed  by  an  elastic  resist- 
ance that  the  piece  will  be  automatically  returned  to  battery 
in  time  for  reloading. 

The  former  class  contains  the  systems  for  which  mobility 
is  essential,  and  the  latter  contains  those  that  are  stationary. 
Some  systems  may  ^be  placed  in  an  intermediate  class, 
requiring  mobility  and  permitting  recoil  of  the  piece  rela- 
tively to  its  support. 

FIRST  CLASS.     MACHINE  GUNS. 

Owing  to  the  desire  to  simplify  the  supply  of  ammunition, 
these  pieces  are  frequently  fitted  to  the  cartridge  used  by 
infantry.  The  conditions  of  transportation  furnish  the 
mass  required.  Their  ballistic  properties  restrict  their 
scope  to  the  zone  of  infantry  fire,  within  which  their  value 
consists  in  the  small  number  of  men  required  for  their  service 


XXIX. — CANNON    WITHOUT    RECOIL. 


and  the  consequent  possibility  of  selecting  the  coolest 
and  most  skillful  men  and  of  protecting  them  from  the 
enemy's  fire. 

The  difficulties  of  transportation  on  land  appear  to  assign 
this  class  to  the  defence,  for  which  service  the  concentra- 
tion of  its  fire  upon  objects  hidden  by  its  own  smoke, 
renders  it  most  valuable. 

To  this  class  in  the  present  U.  S.  Service  belong  the 
Gatling  and  the  Gardner  machine  guns,  which  use  the  same 
ammunition  as  the  service  rifle,  and  the  Hotchkiss  Revolving 
Cannon,  firing  an  explosive  projectile  such  as  described 
Chapter  XVI. 

THE    GATLING    GUN. 

Construction. 

This  gun  consists  essentially  of  a  cluster  of  parallel  mag- 
azine bolt  guns  grouped  cylindrically  about  an  axial  shaft 
to  which  they  are  attached  by  circular  diaphragms  called 
barrel  plates.  Each  member  of  the  combination  is  inde- 
pendent of  the  others  except  that  the  magazine  is  common 
to  them  all. 

The  rotation  of  a  hand  crank  attached  to  the  shaft  brings 
each  member  in  succession  opposite  to  the  mouth  of  the 
magazine  where  it  is  loaded,  and  operates  the  bolts  so  that 
they  progressively  perform  the  functions  noted  in  Chapter 
XXVIII. 

The  manner  in  which  this  is  accomplished  is  as  follows; 
see  figures  1,  2. 

'  Fixed  upon  the  shaft,  6*,  in  rear  of  the  barrels  is  a  com- 
posite fluted  cylinder,  C,  each  flute  in  which  corresponds 
to  the  well  of  tiliej  receiver.  Each  flute  carries  a  bolt, 
Z,  containing  the  essentials  of  the  lock  for  a  bolt  gun.  The 
firing  pin  is  peculiar  in  that  it  passes  through  the  bolt  and 
terminates  in  a  knob  in  rear. 


XXIX.— CANKON  WITHOUT  kECOlL. 


From  the  rear  of  each  bolt  projects  a  radial  lug.  corre- 
sponding to  the  handle  of  the  ordinary  rifle.  These  lugs 
enter  a  cam  groove  fixed  within  the  casing  that  surrounds  the 
fluted  cylinder.  This  groove  is  essentially  an  oblique  section 
of  the  casing,  the  highest  point  of  the  section  being  in  rear. 

The  constraint  of  the  flutes  and  of  the  groove  commutes 
the  continuous  rotation  of  the  cluster  of  bolts  with  respect 
to  the  axis,  into  intermittent  reciprocating  motion  with 
respect  to  the  barrel  to  which  each  bolt  belongs.* 

The  upper  and  lower  segments  of  the  cam  groove  have 
their  planes  at  right  angles  to  the  axis  of  revolution  so  that 
the  developed  groove  is  of  the  form  shown  in  figure  3.  The 
resulting  arcs  may  be  termed  the  advancing  and  retiring  seg- 
mentSy  a  and  r,  and  the  loading  and  firing  flats^  I  and  f. 
The  flats  give  the  intermittent  motion  desired  by  interrupt- 
ing the  reciprocating  motion  cf  the  bolts;  in  the  first  case 
to  allow  the  cartridge  time  to  fall  before  the  bolt,  and  in 
the  second  case  to  allow  for  the  event  of  a  cartridge  **  hang- 
ing fire."  Such  concentric  surfaces  are  frequently  found  in 
the  cams  used  in  machine  guns. 

The  firing  flat  is  at  a  distance  in  rear  of  the  barrels  exactly 
equal  to  the  length  of  the  bolt;  the  loading  flat  is  in  rear  of 
the  firing  flat  at  a  distance  a  little  greater  than  that  of  the 
cartridge.     See  figure  2. 

The  exterior  casing,  which  supports  the  ends  of  the  shaft, 
the  crank  and  the  trunnions,  is  pierced  above  the  front  end 
of  the  cylinder  to  admit  cartridges  from  a  detachable  maga- 
zine for  which  the  casing  provides  a  seat. 

The  sear  is  replaced  by  a  grooved  cocking  rib,  R,  figure  3, 
into  which  the  knob  passes  as  the  bolt  advances  along  the 


*  The   principle  has  already  been  seen  in  the  guide  curve  of  the 
torsional  testing  machine,  Chapter  XV. 


XXIX. — CANNON   WITHOUT   RECOIL. 


segment,  a.  Just  as  the  coiled  mainspring  attains  its  maximum 
compression  the  lug  on  the  bolt  enters  the  firing  flat,  and 
the  termination  of  the  cocking  groove  allows  the  firing  pin 
to  fall. 

The  retraction  of  the  firing  pin  and  the  extraction  and 
ejection  of  the  empty  shell  are  effected  by  means  similar  to 
those  already  described  for  the  small  arm. 

It  is  significant  to  observe  how  closely  the  latest  type  of 
the  magazine  arm  approaches  the  principles  of  the  Gatling 
gun,  the  essential  features  of  which  have  not  been  changed 
since  its  appearance  in  1865. 

Eemarks. 

Each  member  is  thus  fired  only  once  In  each  revolution, 
but  the  number  of  members  (5  or  10)  is  such  that  while  the 
individual  feed  is  deliberate,  the  collective  fire  is  rapid. 

The  bolts  are  interchangeable  and  can  be  readily  removed 
and  replaced.  Being  independent  of  each  other,  the  removal 
of  a  disabled  bolt  affects  only  the  intensity  of  the  fire. 

The  crank  handle  may  be  attached  directly  to  the  shaft, 
or,  when  power  rather  than  rapidity  is  required,  to  a  worm 
gear  on  a  shaft  at  right  angles  to  the  main  shaft,  as  shown 
in  figure  1.  In  the  latter  case  each  revolution  of  the  crank 
causes  one  member  to  fire,  whereas  in  the  former  case  the 
number  of  shots  fired  in  each  revolution  of  the  crank  is  equal 
to  the  number  of  the  barrels. 

Mounts. 

The  gun  is  mounted  on  a  universal  joint  so  that  it  may 
be  trained  i.  e.  moved  in  azimuth,  without  disturbing  the 
position  of  the  trail. 

Instead  of  the  wheeled  carriage  a  tripod  is  sometimes 
used,  as  in  mountain  warfare;  but,  though  light,  its  want  of 
mobility  is  objectionable. 


XXIX. — CANNON    WITHOUT    RECOIL. 


The  Magazine. 

With  good  ammunition  the  efficiency  of  the  arm  depends 
largely  upon  the  efficiency  of  the  feed,  and  this  upon  the 
form  of  magazine  employed. 

X.     THE    FEED    CASE, 

In  the  earlier  models  the  magazine,  or  feed  case,  consisted 
of  a  tin  prism  of  trapezoidal  cross  section  containing  40 
cartridges  lying  horizontally  one  above  the  other,  as  in  the 
Lee  magazine,  inverted.  These  were  surmounted  by  a 
weight  provided  with  a  projecting  thumb-piece  to  which  an 
assistant  could  apply  the  pressure  necessary  to  prevent  the 
dislocation  of  the  column  from  the  shock  of  falling  and  of 
firing. 

In  practice  it  was  found  difficult  to  prevent  a  cartridge 
from  occasionally  entering  the  flutes  obliquely  and  thus 
jamming  the  gun;  also,  the  longitudinal  component  of  the 
weight  varied  with  the  inclination  of  the  gun.  The  risli  of 
jamming  tended  to  retard  the  firing,  which  was  further 
delayed  by  the  time  required  to  refill  the  empty  feed  cases. 

2.  THE  BRUCE  FEED.   FIGURE  4 

This  consists  of  two  parts. 

First,  a  coarsely  toothed  wheel  revolving  loosely  in  the 
hopper  just  below  the  mouth  of  the  magazine.  This  guides 
the  cartridges  from  the  magazine  to  the  fluted  cylinder  and 
keeps  their  axes  parallel  to  that  of  the  shaft.  It  may  be 
used  with  all  magazines. 

Second,  the  detachable  feed  case  is  replaced  by  a  semi- 
permanent bronze  standard,  figure  5.  The  front  face  of  this 
contains  two  T  sliaped  grooves  so  arranged  as  to  hold  two 
parallel  columns  of  cartridges  horizontally    by   the   flanges 


XXIX. CANNON    WITHOUT    RECOIL. 


around  the  heads  of  the  cartridges.  The  grooves  are  readily 
filled  by  entering  into  them  the  heads  of  the  cartridges  con- 
tained in  the  pasteboard  boxes  in  which  they  are  issued  to 
the  troops. 

By  pulling  off  the  box  at  right  angles  to  the  grooves  the 
cartridges  are  left  hanging  in  the  position  desired.  Under 
pressure  from  above,  the  grooved  piece  swings  aside  as  each 
groove  is  alternately  emptied  and  directs  the  remaining  column 
into  the  hopper. 

This  arrangement  enables  the  fire  to  be  maintained  as  long 
as  the  general  supply  of  ammunition  for  the  troops  is  available. 

3.     THE    ACCLES'    FEED    DRUM.       FIGURE   5. 

This  consists  of  a  cylinder  having  two  heads  which  are 
at  a  distance  apart  about  equal  to  the  length  of  a  cartridge. 
On  the  inside  of  each  head  is  a  spiral  groove  *  the  pole  of 
which  is  in  the  axis  of  the  drum,  and  the  radial  interval 
between  the  spires  is  equal  to  the  diameter  of  that  end  of 
the  cartridge  in  contact  with  the  head. 

Around  the  axis  of  the  drum  lie  the  radial  arms  of  the 
propeller.  These  divide  the  interior  of  the  drum  into  sectors, 
each  of  which  contains  a  number  of  cartridges  equal  to  the 
number  of  intersected  spires.  The  ends  of  the  arms  project 
beyond  the  outer  groove  suflnciently  to  engage  with  the 
flutes  of  the  cylinder,  so  that  when  this  cylinder  revolves 
the  spiral  groove  is  emptied  from  the  outer  end. 

Thefeedisthusindependentof  gravity,  and  the  connection 
between  the  fluted  cylinder  and  the  propeller  arms  is  such 
that  each  cartridge  as  it  emerges  from  the  drum  is  carried 
parallel  to  itself  and  tangentially  into  the  corresponding 
flute.     The  synchronism  thus  attained  permits  the  gun  to 


*  The  spiral  is  not  truly  geometrical,  as  seen  by  the  figure. 


XXIX. — CANNON    WITHOUT    RECOIL. 


be  fired  with  certainty  at  any  angle  of  elevation,  and  at  a 
speed  that  is  limited  only  by  the  rapidity  with  which  the 
crank  can  be  turned.  It  has  been  fired  at  the  rate  of  2000 
rounds  per  minute  and  also  at  a  elevation  of  87  degrees. 

The  objections  to  the  drum  refer  to  its  bulk  and  to  the 
(time  lost  in  refilling  it.     It  contains  104  cartridges. 

THE    GARDNER    GUN.       FIGURES    6,    7. 

This  consists  essentially  of  two  or  more  bolt  guns  placed 
side  by  side,  and  surmounted  by  a  magazine  resembling  the 
Bruce  feed  guide,  but  without  the  valve. 

The  bolts  are  operated  by  a  transverse  crank  shaft,  or  lock 
cam,  turned  by  a  handle  outside.  The  cranks  are  at  180 
degrees  from  each  other,  and  their  crank  pins,  figure  7,  ^, 
work  in  vertical  U  shaped  pieces  in  which  the  base  of  the 
bolts  are  formed. 

The  contact  surfaces  of  the  notches  are  partly  concentric 
and  partly  eccentric  with  respect  to  the  crank  shaft;  just 
as  the  cam  groove  of  the  Gatling  is  partly  at  right  angles, 
and  partly  oblique  to  the  axis  of  revolution.  So  long  as  the 
contact  surfaces  are  eccentric  the  rotation  of  the  crank  will 
cause  one  bolt  to  advance  and  the  other  to  retire. 

When  the  crank  pins  are  approaching  the  axis  of  the  bore 
the  contact  surfaces  become  concentric;  the  bolts  then  be- 
come stationary;  on  one  side  to  allow  the  cartridge  to  be 
fired,  and  on  the  other  side  to  allow  the  next  cartridge  to  fall 
into  the  well. 

The  reciprocating  motion  of  the  bolts  operates  a  valve 
that  allows  the  cartridges  to  descend  in  alternate  succession 
from  the  grooves  in  the  magazine.  The  valve  swings  hori- 
zontally under  the  lid.     See  figure  7. 

The  advantages  of  the  arm  are  its  lightness,  and  the  sim- 
plicity and  accessibility  of  the  mechanism;  as  the  lid  cover- 


XXIX. — CANNON    WITHOUT    RECOIL. 


ing  the  Interior  can  be  readily  raised.  On  the  other  hand 
the  rapidity  of  fire  is  much  less  than  that  of  the  Gatling, 
since  the  number  of  barrels  is  less;  and  the  dependence  of 
the  feed  upon  the  operation  of  both  the  bolts  causes  the 
gun  to  be  disabled  by  accidents  to  its  ammunition. 

THE    NORDENFELT   MACHINE   GUN. 

This  arm,  principally  used  in  the  British  Navy,  has  2,  4, 
or  more  barrels  arranged  in  a  horizontal  plane.  In  rear  is 
a  corresponding  row  of  bolts  moved  back  and  forth  together 
by  a  horizontal  hand  lever.  The  feed  is  by  gravity  through 
a  series  of  hoppers,  one  of  these  standing  over  the  well  of 
each  receiver. 

The  firing  is  practically  by  volley,  although  the  interval 
between  the  discharges  may  be  varied  by  the  rapidity  with 
which  the  lever  is  worked. 

Accidents  are  said  to  have  occurred  from  the  explosion  of 
the  magazine  by  the  flame  escaping  from  defective  cartridges, 
and  igniting  the  ammunition  in  the  adjacent  magazine. 

THE  MAXIM  AUTOMATIC  MACHINE  GUN.    FIGURES  8,  9,  10,  11. 

The  distinguishing  feature  of  this  arm  is  its  continuous 
operation  by  the  force  of  the  discharge,  and  the  necessarily 
continuous  supply  of  the  ammunition  afforded  by  the  nature 
of  the  magazine. 
Peed. 

The  magazine  consists  of  a  series  of  belts,  made  of  two 
long  strips  of  tape  riveted  together  at  intervals  sufficient  to 
hold  single  cartridges  between  them.  Each  belt  contains 
334  cartridges,  and,  as  they  may  be  linked  together,  the 
supply  is  continuous.  The  belt  is  fed  transversely  through 
the  gun  so  that  the  cartridges  occupy  successively  a  fixed 


XXIX. — CANNON    WITHOUT    RECOIL. 


position  over  the  chamber.  From  this  position  they  are 
automatically  transferred  to  the  chamber  from  which  they 
are  fired. 

Immediately  'beneath  the  chamber  is  the  ejecting  tube 
through  which  the  empty  shells  are  successively  passed  for- 
ward and  dropped  to  the  ground. 

Construction  and  Operation. 

Omitting  many  important  particulars,  the  operation  of  the 
arm  is  as  follows: — 

Construction. — The  barrel  is  secured  to  a  frame  that  has  a 
slight  sliding  motion  from  front  to  rear  in  the  exterior  casing. 
In  the  rear  end  of  this  frame  is  journalled  a  double  crank, 
figure  8.  The  crank  pin  is  connected  by  a  connecting  rod 
with  the  breech-block  in  front.  The  breech-block  slides 
longitudinally  within  the  frame  to  a  greater  extent  than  the 
frame  slides  within  the  casing. 

The  ends  of  the  crank  shaft  project  through  the  casing 
and  are  utilized  as  follows: — 

On  one  end  is  an  arm,  d^  pointing  downward  and  attached 
at  its  lower  end  by  a  short  chain,  ^,  to  a  powerful  spiral 
spring,/,  the  front  end  of  which  is  fixed  to  the  casing. 

On  the  other  end  is  a  curved  arm,  /,  pointing  upward 
and  lying  in  front  of  a  stop,  g^  rigidly  fixed  to  the  casing. 
On  the  same  end  of  the  crank  shaft,  but  outside  of  /  is  a 
handle,  h.  This  handle  receives  from  the  crank  a  recipro- 
cating motion  of  nearly  180  degrees,  being  limited  on  one 
side  by  the  flat  spring,  b,  and  on  the  other  by  the  latch,  / 
The  space,  o^  shows  the  distance  to  which  the  frame  can 
recoil. 

Before  firing,  the  tension  of  the  spring,/,  brings  the  breech- 
block in  contact  with  the  barrel  and  forces  the  latter  to  its 
foremost  position.     The  crank,  crank  pin  and  the  connect- 


10  5txtx.— cannom  without  recoil. 


ing  rod  are  then  in  the  horizontal  plane  containing  the  axis 
of  the  barrel. 

Operation. — When  the  piece  is  fired  (by  pressing  with  the 
thumb  on  the  trigger,  /,  meanwhile  directing  the  aim  with 
the  handles,  m^  the  barrel  and  frame  with  the  included 
parts  begin  to  recoil  together. 

This  motion  brings  the  curved  arm,  /,  against  the  stop,  ^, 
and  rotates  the  crank  downward  with  a  motion  which  is 
accelerated  by  the  curvature  of  /.  In  so  doing  the  connection 
between  the  crank  and  the  breech-block  draws  back  the  latter 
faster  and  further  than  the  barrel  moves,  and  thus  leaves  room 
for  the  cartridge  to  be  loaded.  At  the  same  time  the  arm,  d^ 
winds  up  on  itself  the  chain  and  puts  on  the  spring,  /,  a 
tension  that  tends  to  restore  the  parts  to  their  original 
position. 

Ako  the  handle,  h^  strikes  the  spring,  b,  which  throws  it 
back  to  the  latch,/,  thereby  assisting  the  restoration  of  the 
parts  by  the  spring,  /.  The  cycle  is  now  complete,  as  far  as 
regards  the  parts  named. 

Feeding. — The  feeding ofthe  ammunition,  which,  from  what 
precedes,  is  seen  to  be  the  motive  power,  is  accomplished  by 
a  peculiar  extractor,  x.  This  slides  up  and  down  in  front  of 
the  breech-block  and,  in  an  undercut  groove  on  its  front 
surface,  holds  two  cartridges  by  their  flanges.  One  cartridge 
is  that  last  fired,  and  the  other  is  that  next  to  be  fired. 

When  the  block  recoils  the  extractor  pulls  out  these  car- 
tridges from  the  chamber  and  the  belt  respectively:  and  just 
before  the  block  advances  the  extractor  drops,  so  as  to  bring 
the  fired  case  opposite  to  the  ejector  tube  and  the  full  car- 
tridge opposite  to  the  chamber. 

After  their  entrance  into  their  respective  cavities  the  ex- 
tractor rises,  leaving  the  flange  of  the  fired  case  unsupported, 
(as  the  undercut  groove  extends  only  over  the  upper  portion 


XXIX. — CANNON    WITHOUT    RECOIL.  11 

of  the  face  of  the  extractor)  and  embraces  another  cartridge 
from  the  belt.  The  latter  has  meanwhile  been  moved  along 
one  interval  by  a  pawl  actuated  by  the  preceding  machinery. 

If,  as  is  usual,  the  pressure  on  the  trigger  be  maintained 
during  these  motions  another  shot  will  be  fired  and  the 
motions  will  be  repeated  as  long  as  the  ammunition  is 
supplied. 

Under  these  circumstances  the  rapidity  of  fire  is  11  shots 
per  second. 

The  operation  of  the  lock  may  be  understood  from  an  in- 
spection of  figure  11.  The  cocking  power  is  applied  to  the 
tumbler  through  a  forked  lever  by  which  the  connecting  rod 
is  attached  to  the  block. 

The  handle,  //,  is  used  to  start  the  gun  firing  or  to  over- 
come the  stoppage  resulting  from  a  misfire. 

As  there  is  but  one  barrel,  which  in  continuous  firing  might 
become  heated  to  excess,  it  is  surrounded  with  a  water  jacket. 
The  recoil  pumps  a  small  quantity  of  water  into  this  at  every 
fire;  it  is  provided  with  holes  for  the  escape  of  the  steam 
generated. 
Advantages. 

The  principal  advantages  of  this  arm  depend  upon  the 
absorption  of  so  much  of  the  energy  of  recoil  by  the  work- 
ing of  the  parts  that  the  weight  of  the  carriage  may  be 
greatly  reduced  without  affecting  its  stability.  The  most 
important  results  from  this  principle  will  be  found  in  its 
application  to  the  field  cannon  hereafter  described. 

Another  advantage  results  from  the  greatly  increased 
dirigibility  of  the  arm,  since  it  may  be  pointed  like  a  hose 
by  the  one  man  required  for  its  service. 

Considering  the  variety  of  the  functions  to  be  performed, 
the  rapid  motion  of  the  parts  and  their  restricted  space,  the 
construction  cannot  be  called  complicated.    In  such  matters 


13  XXIX. — CANNON    WITHOUT    RECOIL. 

it  is  better  to  seek  simplicity  of  service  tlian  excessive  sim- 
plicity of  construction. 

GENERAL    REMARKS    ON    MACHINE    GUNS. 

Owing  to  the  excitement  prevailing  during  the  few 
moments  when  rapidity  of  fire  is  of  the  greatest  importance 
the  efficiency  depends  mainly  upon: — 

1.  The  quality  of  the  ammunition,  the  food. 

2.  The  certainty  of  its  supply,  the  feed. 

3.  The  facility  with  which  the  aim  may  be  changed,  or 
the  dirigibility  of  its  fire. 

1.  The  Food. 

When  compared  with  ordinary  field  artillery  the  range 
and  power  of  the  infantry  ammunition  is  so  limited,  the 
correction  of  the  aim  so  difficult,  and  the  moral  effect  of 
solid  projectiles  so  small  that  machine  guns  of  small  caliber, 
although  rendered  popular  by  their  great  mechanical  effi- 
ciency, will  probably  in  service  be  relegated  to  the  subordi- 
nate purposes  of  the  defense,  and  for  use  against  an  enemy 
unprovided  with  artillery. 

When  compared  with  infantry  operating  in  broken  or 
wooded  ground  their  deficient  mobility  would  often  render 
them  an  obstruction  rather  than  a  help;  since  only  under 
exceptional  circumstances  can  they  maintain  their  own 
defense. 

Owing  to  the  suddenness  with  which,  in  order  to  produce 
a  decisive  effect,  their  services  are  required  it  has  been  pro- 
posed to  attach  them  to  small  tactical  units  of  infantry  and 
cavalry;  but  the  objections  above  cited  and  the  evident 
difficulty  of  administering  such  scattered  commands  would 
probably  cause  this  plan  to  fail,  as  did  the  system  of 
battalion  guns,  which,  after  trial  in  the  Seven  Years  War,  was 
abandoned. 


XXIX. — CANNON    WITHOUT    RECOIL.  13 

The  transport  of  the  large  amount  of  ammunition  that 
machine  guns  require  compels  the  use  of  wheeled  draught 
(except  in  the  mountain  service)  and  therefore  assigns  them 
to  the  artillery.  The  question  then  arises,  whether,  having 
a  given  supply  of  men,  horses  and  money,  these  means  may 
not  be  better  utilized  in  the  legitimate  sphere  of  the  artillery 
rather  than  in  providing  a  defensive  arm  of  only  occasional 
utility.  The  preponderance  of  opinion  seems  to  be  adverse 
to  the  general  employment  of  machine  guns  of  small  caliber, 
and  shows  that  mechanical  perfection  must  be  subordinated 
to  tactical  utility. 

In  the  war  of  1870  they  were  speedily  silenced  by  the 
German  artillery  and  have  not  since  been  organized  for 
service  in  any  European  army.  For  naval  purposes,  where 
the  difficulties  of  supply  hardly  exist,  and  where  the  deploy-. 
ment  of  a  firing  line  is  impossible,  their  value  is  greater, 
although  here  they  are  giving  way  to  the  rapid  firing  guns 
to  be  described. 

2.  The  Feed. 

The  great  rapidity  with  which  the  gun  is  operated  is  apt 
to  lead  to  "jamming"  in  case  a  cartridge  should  from  any 
cause  fail  to  enter  its  proper  chamber.  The  injury  will  be 
aggravated  from  the  natural  tendency  in  moments  of  excite- 
ment to  overcome  the  obstruction  by  force.  To  this  cause 
may  be  attributed  grave  complaints  made  against  these  guns 
during  the  recent  fighting  in  the  Soudan. 

3.  Dirigibility. 

The  dirigibility  of  these  guns,  except  the  Maxim,  is  im- 
paired by  the  necessity  of  temporarily  clamping  them  to  resist 
the  deflection  due  to  the  operation  of  the  crank.  The  accu- 
racy is  also  impaired  by  vibrations  due  to  firing. 

The  fire  may  be  distributed  by  oscillating  the  piece  ui  a 


14  XXIX. — CANNON    WITHOUT    RECOIL. 

plane  parallel  to  the  axle;  but,  if  the  line  fired  at  be  oblique 
to  this  plane  it  will  be  cut  at  but  one  point.  The  difficulty  of 
sweeping  a  curved  or  oblique  line  is  increased  by  the  screen 
of  smoke  and  by  the  uncertainty  of  the  point  of  nnpact. 

In  the  Maxim  gun  these  objections  only  partly  apply, 
since  the  pointing  of  the  gunner  is  not  interfered  with  by 
the  motions  of  the  men  at  the  magazine  and  at  the  crank. 

THE    HOTCHKISS    REVOLVING    CANNON.       FIGURES    12,  13. 

In  its  mechanical  construction  this  resembles  the  Gatling 
gun,  but,  as  it  fires  an  explosive  projectile,  it  occupies  a  place 
intermediate  between  the  machine  guns  proper  and  the  rapid 
fifing  guns  to  be  described. 

It  uses  primed  metallic  ammunition  of  a  caliber  the  in- 
ferior limit  of  which  for  explosive  projectiles  was,  from 
reasons  of  humanity,  fixed  by  International  Convention  at 
about  one  pound,  and  the  superior  limit  of  which  is  deter- 
mined by  the  difficulties  of  the  feed. 
Operation. 

The  continuous  revolution  of  the  transverse  crank  shaft 
causes  the  cluster  of  five  barrels  to  revolve  intermittently  in 
one  direction.  The  interruption  in  the  rotation  enables  the 
single  breech  mechanism,  whose  motion  is  continuous,  to 
serve  each  barrel  in  succession,  by  simultaneously  firing  one 
barrel,  loading  another  and  extracting  the  empty  cartridge 
case  from  a  third,  while  the  cluster  is  at  rest.  These  oper- 
ations are  performed  at  every  rotation  of  the  crank,  during 
half  of  which  period  the  cluster  is  at  rest. 

The  cartridge  is  supported  by  a  r.tationary  breech,  in  front 
of  which  the  cartridges  circulate  an  i  through  which  the  firing 
pin  passes  at  the  lowest  point. 

The  feed  is  by  gravity  through  a  trap  door,  which,  being 
raised  by  the  advance  of  the  loading  bolt,  admits  but  one 


XXIX. — CANNON    WITHOUT    RECOIL.  15 

cartridge  at  a  time.     The  rapidity  of  fire  is  from  30  to  60 

per  minute. 

Remarks. 

The  gun  compensates  for  the  relative  infrequency  of  its 
fire  by  the  use  of  an  explosive  projectile,  each  fragment  of 
which  may  cause  a  hit.  This  permits  the  aim,  which  is 
normally  deliberate,  to  be  further  corrected  by  ob.erving 
the  point  at  which  the  projectile  explodes.  A  percussion 
fuze  is  used. 

The  strength  of  the  parts  of  the  breech  mechanism  and 
their  accessibility  compensate  for  the  dependence  of  the 
performance  of  the  gun  as  a  whole  upon  that  of  each  of  its 
constituent  parts. 
Employment. 

The  Revolving  Cannon  was  originally  devised  to  defend 
vessels  from  the  attacks  of  swift  torpedo  boats,  the  time 
allowed  for  firing  at  which,  between  their  discovery  and  the 
impact  of  their  torpedoes,  might  not  exceed  two  minutes. 

It  has  been  attempted  to  introduce  it  into  the  field  service; 
but  the  relation  between  the  caliber  and  the  weight  of  the 
piece  and  carriage  has  so  far  prevented  its  systematic  adop- 
tion. For,  while  in  the  naval  service  perforation  is  of  the 
utmost  importance,  and  the  operation  of  the  percussion  fuze 
is  rendered  certain  by  the  nature  of  the  object  first  struck; 
in  the  field  the  use  of  shrapnel  ignited  by  an  adjustable  time 
fuze  against  animate  objects  is  more  important,  since  against 
defenses  the  Hotchkiss  shell  is  powerless.  Against  field 
defenses  indeed,  it  is  curved  fire  with  reduced  charges  and 
large  projectiles  that  is  required,  rather  than  the  flat  trajectory 
needed  for  penetration. 

For  these  reasons  the  Revolving  Cannon  has  been  princi- 
pally confined  to  the  naval  service,  in  which  during  the  war 
between  France  and  China,  in  1881,  it  was  most  effective. 


16  XXIX. — CANNON    WITHOUT    RECOIL. 

An  exception  may  be  made  as  to  its  use  in  defending  capon- 
nieres,  for  which  purpose,  as  the  range  is  constant  and  mo- 
bility IS  not  necessary,  the  gun  is  well  adapted.  In  this 
service  canister  is  employed,  and  the  barrels  have  each  a 
different  twist  so  as  to  distribute  their  fire  with  uniformity 
over  the  area  to  be  swept. 

SECOND  CLASS.     RAPID  FIRING  GUNS. 

These  are  single  barreled  and  may  be  classified  according 
to  the  means  by  which  they  are  loaded  as: — 

1.  Hand  served,  or  non-automatic. 

2.  Automatic,  in  varying  degrees. 
Object. 

These  arms  may  be  said  to  have  been  developed  from  the 
later  type  of  machine  guns  by  the  improvements  in  the 
offensive  and  defensive  power  of  torpedo  boats.  Their 
proper  employment  on  shore  has  yet  to  be  determined;  but 
in  the  naval  service,  in  which  their  development  is  limited 
only  by  the  weight  of  the  ammunition  to  be  handled,  they 
have  rapidly  increased  from  the  comparatively  recent  1  pdr. 
and  6  pdr.  to  the  6  in.  100  pdr.,  and  have  made  great 
changes  necessary  in  the  armament  of  vessels.* 

*  As  the  power  of  the  gun  Jincreased,  the  weight  of  the  armor  in- 
creased so  that  but  few  vessels  are  able  to  carry  enough  armor  to  protect 
the  entire  surface  exposed  to  fire.  The  armor  is  therefore  often  concen- 
trated over  the  vital  portions,  and  the  ends  left  with  little  or  no  protection. 
Against  the  light  armor  required  by  these  conditions,  and  now  generally 
used,  the  rapid  fire  of  guns  small  enough  to  be  easily  directed  and  large 
enough  to  carry  an  effective  bursting  charge,  would  be  very  destructive. 
Compared  with  a  heavier  caliber,  the  aim  could  be  more  easily  corrected, 
the  number  of  rounds  for  a  given  stowage  capacity  be  increased,  and  the 
striking  energy  of  the  shell  being  sufficient  to  penetrate  the  target,  their 
explosion  would  riddle  it  sufficiently  to  endanger  the  stability  of  the  vessel. 
The  effect  would  be  increased  by  repeated  impact  in  the  same  spot  so  that, 


XXIX. — CANNON   WITHOUT   RECOIL.  17 

The  Italian  ironclad  "Piemonte"  built  in  England  in 
1889,  is  the  most  striking  illustration  of  the  principle  in- 
volved. In  a  given  time  she  can  fire  more  than  twice  as 
great  a  weight  of  metal  as  any  vessel  afloat,  including  those 
costing  five  or  six  times  as  much.  The  33  pounder  with 
which  she  is  largely  armed  has  hit  a  target  6  feet  square 
five  times  in  succession  in  81  seconds  at  a  range  of  1300 
yards.  Suppose  the  target  to  be  a  torpedo  boat,  advancing 
to  attack  the  vessel  carrying  the  gun  at  a  speed  of  20  knots 
per  hour,  (35  f.  s.)  and  capable  of  effectively  discharging 
its  torpedo  at  a  distance  of  300  yards;  she  would  be  under 
fire  for  86  seconds,  during  which  time  20  shots  might  be 
fired,  as  against  2  or  3  shots  from  an  ordinary  breech  load- 
ing cannon.  A  similar  advantage  would  follow  great  rapidity 
of  fire  at  the  ports  of  an  armored  structure  during  the  short 
time  that  they  would  be  exposed  to  fire.  There  would  be 
not  only  the  chance  of  entering  the  port  with  shell,  but  that 
of  disabling  the  gun,  as  it  has  been  found  that  the  chase  of 


principally  on  account  of  their  accuracy,  the  aggregate  effect  in  a  given 
time  produced  by  a  given  weight  of  rapid  fire  guns  would  be  greater  than 
that  of  a  smaller  number  of  heavy  cannon.  The  question  involves  the 
determination  of  the  best  utilization  of  that  fraction  of  the  entire  displace- 
ment of  the  vessel  that  is  allowed  for  its  offensive  power.  This  is  small, 
being  in  the  neighbourhood  of  7  per  cent. 

For  the  reasons  given  Chapter  XVI,  page  21,  armor  piercing  pro- 
jectiles are  becoming  more  and  more  restricted  in  their  "mining  power." 
It  is  thought  that  a  4  inch  plate  of  the  best  quality  will  explode  any  high 
explosive  fired  against  it  as  a  bursting  charge,  before  penetration  is 
effected. 

From  what  precedes  it  will  appear  that  the  present  state  of  the  question 
is  that  of  a  reaction  from  the  idea  which  considers  the  ship  as  but  a  float- 
ing carriage  for  the  heaviest  gun  that  it  can  carry. 

When  tested  in  battle  the  truth  will  probably  be  found  to  lie  between 
the  two  extremes,  and  the  best  results  to  be  obtained  by  a  proper  appli- 
cation of  the  principle  of  the  independence  of  function. 


18  XXIX.— CANNON    WITHOUT    RECOIL. 

a  modern  gun  can  be  penetrated  by  the  armor-piercing  pro- 
jectiles fired  from  R.  F.  guns. 

One  great  advantage  of  these  guns  would  be,  that  as  the 
attacking  vessel  approached  and  as  therefore  the  flatness  of 
the  trajectory  increased,  the  elevation  would  not  require 
sensible  adjustment  between  shots,  and  the  target  could  be 
"followed"  by  the  gunner;  his  eye  being  on  the  sights,  his 
finger  on  the  trigger,  and  the  piece  being  directed  by  the 
motions  of  the  body  as  hereafter  described. 

GENERAL    PRINCIPLES. 

The  development   of  R.  F.  guns  has  followed  improve- 
ments in  the  ammunition  and  in  the  7tiounts,  as  are  called 
the  means  of  supporting  and  directing  the  gun. 
Ammunition. 

Rapidity  of  fire  results  from  the  use  of  a  simple  fermeture 
in  connection  with  self  primed  metallic  ammunition  con- 
structed on  the  same  principle  as  that  used  in  small  arms. 

The  size  of  the  cartridges  is  now  limited  only  by  the  diffi- 
culty of  expeditiously  handling  tl  m.  That  for  the  33  pdr., 
containing  about  12J  lb.  of  powc  jr  and  weighing  complete 
about  50  lbs.,  is  as  heavy  as  one  man  can  load  with  ease. 
That  for  the  70  pdr.  requires  the  united  efforts  of  two  men, 
the  greatest  number  that  can  be  employed  about  the  breech 
without  interfering  with  the  gunner.  For  large  calibers  the 
projectile  is  sometimes  loaded  separately;  in  this  case  rapid- 
ity of  fire  depends  solely  on  the  mount. 
Mounts. 

The  mounts  are  of  two  classes,  depending  upon  the  rela- 
tion between  the  energy  of  the  recoil  and  the  character  of 
the  emplacement.  When  the  latter  is  relatively  strong 
Non-Recoil  Mounts  may  be  used,  as  in  firing  light  guns  from 


XXIX. — CANNON    WITHOUT    RECOIL.  19 

ships  and  heavier  guns  from  masonry  emplacements.  The 
structural  elasticity  of  these  mounts  absorbs  the  recoil  and 
returns  the  piece  to  battery. 

When  the  emplacement  is  not  rigid  enough  to  resist  the 
recoil,  Recoil  Mounts  must  be  used,  as  in  the  field  service. 
In  these  springs  or  hydraulic  buffers  distribute  the  pressure 
over  a  longer  path  than  in  the  former  case. 

In  all  cases  the  aim  is  corrected  by  a  crutch  shaped  stock 
which  the  gunner  holds  against  his  shoulder  with  one  hand, 
while  the  other  hand  rests  on  the  trigger. 

The  piece  thus  becomes  almost  as  dirigible  as  a  small 
arm,  and  is  particularly  adapted  for  firing  from  an  oscillat- 
ing platform  at  objects  with  relative  motion,  as  in  naval 
combats.  In  non-recoil  mounts  the  stock  may  be  faster.jd 
to  the  gun,  but  in  the  other  class  it  must  be  fastened  to  the 
mount. 

Figure  14  shows  a  crinoline  or  cone  non-recoil  mount;  and 
figure  15  a  type  of  the  recoil  mount.     In  this  figure,  b,  is 
the  buffer  and,  j-,  s^  springs  intended  to  return  the  piece  to 
battery  by  their  action  on  the  bent  levers,  /,  /. 
Hotchkiss  Mountain  Carriage. 

Figure  16  shows  a  non-recoil  mount  for  a  mountain  car- 
riage. The  carriage  as  a  whole  is  kept  from  sliding  by  the 
brake  and  by  a  transverse  plate  under  the  trail  plate  called 
the  spade.  The  spade  may  be  sunk  into  the  ground  by  the 
weight  of  a  man  standing  on  the  wifigs  of  the  trail  plate, 
and  by  that  of  the  gunner  on  the  seat. 

The  cheeks  are  unusually  high,  permitting  the  gun  to  be 
fought  without  wheels  in  exposed  positions.  A  slight  play 
in  azimuth  is  allowed,  since  this  greatly  facilitates  aiming, 
and  the  lateral  component  of  the  recoil  is  insufficient  to 
affect  the  stability  of  the  piece. 

To  facilitate  transportation  the  stock  is  in  two  pieces. 


20  XXIX. — CANNON    WITHOUT    RECOIL. 

The  elevating  gear  is  detachable;  when  used  without  it. 
the  system  resembles  a  large  pistol  on  wheels. 
Hotchkiss  Field  Carriage. 

Figure  17  shows  a  recoil  mount;  the  carnage  consisting 
of  three  main  parts  and  the  wheels. 

These  parts  are: — 

1.  The  stock,  s,  secured  to  the  axle. 

2.  The  chassis,  ^,  which  has  a  limited  motion  in  azimuth 
by  means  of  the  training  screw^  T. 

The  top  carriage,  t  c^  to  which  is  attached  the  ele- 
vating screw,  e. 
The  top  carriage  is  allowed  considerable  recoil  on  the 
chassis;  being  limited  by  the  buffer^  b,  and  restrained  by  three 
oblique  spiral  springs  on  each  side.  These  are  fastened  at  one 
end  to  the  top  carriage  and  at  the  other  end  to  the  chassis. 
Powerful  brakes,  B^  B,  lock  the  wheels  and  are  assisted 
by  the  spade.    The  brakes  are  connected  by  the  brake  bar., 
This  is  slung  from  the  axle  by  two  rods,  so  that  in  march- 
ing it  may  be  hooked  up  under  the  trail. 

CONSTRUCTION    OF    THE    AMMUNITION. 

Cartridge  Case. 

This  may  be  either  solid  drawn  as  in  small  arms,  or  built 
up.  In  the  latter  case,  for  economy,  the  tube  forming  the 
body  is  bent  in  at  the  base  and  riveted  between  two  cups 
by  a  wrought  iron  disc  that  forms  the  head,  as  shown  in 
figure  18.*  For  greater  certainty  of  fire  the  primer  is  renewed 
at  every  reloading. 
Drill  Cartridge. 

That  shown  in  figure  19  is  of  soft  material  formed  to  the 
full  size  of  the  cartridge  about  a  section  of  the  service  musket 

*  It  is  now  proposed  (1890)  to  electro-weld  the  head  to  the  bottom  of 
the  tube. 


XXIX. — CANNON    WITHOUT    RECOIL.  21 

barrel.    From  this  barrel  the  service  cartridge  may  be  fired 
at  drill.     This  familiarizes  the  gunners  with  the  service  of 
the  piece  in  action  without  requiring   the   great   expense 
attending  the  use  of  the  regular  ammunition. 
Projectiles. 

Shell  and  shrapnel  are  provided.  The  former'use  a  base 
percussion  fuze  and  are  either  of  cast  iron  or  of  forged  and 
tempered  steel  according  to  the  use  required  of  them. 

CONSTUCTION   OF   THE    GUN    AND    FERMETURE.    ^ 

Gun. 

Except  for  the  smallest  calibers,  this  is  a  built  up  steel 
gun,  the  type  of  which  for  medium  calibers  is  represented  in 
figure  20. 

The  jacket  carries  both  breech-block  and  trunnions  so  as 
to  relieve  the  tube  from  longitudinal  stress.     The  enlargement 
of  the  jacket  in  rear  increases  the  bearing  surface  of  the 
breech-block. 
Fermeture.    Figures  21,  22,  23,  24,  25. 

This  resembles  that  of  the  mountain  gun  already  described; 
but  it  differs  from  it  in  that  the  motion  of  the  block  being 
vertical,  its  own  weight  helps  to  open  it.  The  mechanism  is 
contained  in  and  about  the  block,  and  is  situated  so  as  to  be 
most  easily  accessible  for  repairs. 

It  consists  of  the  following  parts : 

B,  the  block,  the  left  side  of  which  contains  three  shallow 
grooves,  viz.: 

g  g  —  the  guide  groove. 

s  g  —  the  s/op  groove. 

X  g  —  the  extractor  groove. 

Note. —  To  the  late  B.  B.  Hotchkiss,  an  American  whose  works  were 
in  France,  is  due  the  first  practical  application  of  the  principle  of  rapid 
fire  guns.  His  system  is  that  generally  used  in  this  work  to  illustrate 
these  principles.  Many  variations  of  his  methods  have  arisen,  some  of 
the  more  important  of  which  will  be  discussed. 


22  XXIX. — CANNON    WITHOUT    RECOIL. 

On  the  right  side  is  another  guide  groove,  g'  g' j  and  s  w, 
the  stud  ivay;  beneath  which  is  a  wide  triangular  recess, 
c  w,  the  crank  way. 

The  double  lever,  L,  is  secured  to  the  crank  shaft,  c  s, 
which  passes  through  the  side  of  the  breech,  and  terminates 
inside  in  the  crank,  c,  on  the  upper  end  of  which  is  the 
stud,  s. 

The  hub  of  the  double  lever  is  formed  into  the  cocking 
toe,  c  t. 

The  hanifner,  h,  is  secured  to  the  rocking  shaft,  r  j,  by  a 
spline  (see  Webster),  so  that  it  may  be  assembled  with  the 
rocking  shaft  and  yet  revolve  certainly  with  it.  The  rock- 
ing shaft  traverses  the  lower  front  quarter  of  the  block. 
Its  right  hand  extremity  forms  the  cocking  arfn,  c  a,  project- 
ing so  as  to  revolve  in  the  same  plane  as  the  cocking  toe 
above  it. 

The  double-leaved  7nain  spring,  in  s,  presses  up  the  rear 
end  of  the  hammer,  and  pulls  it  down  in  front  through  the 
swivel,  s  V,  thus  diminishing  the  friction  of  the  rocking  shaft 
in  bearings.  The  main  spring  is  kept  from  moving  as  a 
whole,  by  engaging  its  folded  end  in  a  notch  in  the  rear 
portion  of  the  block. 

The  sear,  s',  is  pivoted  to  the  block  just  below  the  rocking 
shaft,  and  is  constantly  pressed  up  by  the  sear  spring,  s  s. 

When  the  block  is  in  place,  the  extremity  of  the  sear 
comes  in  contact  with  the  front  end  of  a  bent  lever  forming 
the  trigger,  T.  This  trigger  plays  in  the  pistol  grip  which 
is  rigidly  connected  with  the  breech. 

Stock.     Figure  14. 

To  the  left  side  of  the  piece  in  non-recoil  guns;  or,  in 
recoil  guns,  to  that  portion  of  the  carriage  which  does  not 
recoil,  is  fastened  the  stock. 


XXIX. — CANNON    WITHOUT    RECOIL.  23 


A  rubber  tube  forms  a  cushion  for  the  gunner's  left 
shoulder. 

The  handles  beneath  serve  for  grasping  with  the  left 
hand  at  different  elevations.  The  right  hand  then  holding 
the  pistol  grip,  the  piece  may  be  aimed  by  the  motions  of 
the  body,  and  fired  at  the  exact  moment  that  the  object  is 
pierced  by  the  line  of  sight. 

OPERATION    OF    THE    FERMETURE. 

To  open  the  Piece. 

Turn  the  most  convenient  handle  to  the  rear.  In  the  first 
portion  of  its  motion  the  crank  stud  travels  in  the  concentric 
portion  of  the  stud-way  so  that  the  block  does  not  move; 
the  direction  of  the  stud-way  then  changing,  further  rotation 
causes  the  block  to  fall  until  it  is  arrested  by  the  stop  screw. 
The  crank  finally  becomes  nearly  horizontal. 

During  the  first  portion  of  the  rotation  of  the  lever  the 
cocking  toe  presses  upon  the  cocking  arm  and  revolves  it, 
and  with  it  the  rocking  shaft  and  hammer,  until  a  notch 
upon  the  rocking  shaft  has  engaged  with  the  sear.  At  this 
moment  the  whole  block,  including  the  hammer,  begins  to 
fall. 

The  extractor  operates  as  in  the  mountain  gun  already 
studied.  Owing  to  the  slight  inclination  of  the  groove  x  g 
to  g  g,  the  first  movements  of  the  extractor  are  relatively 
slow,  developing  great  power.  Ejection  follows  when  the 
abrupt  change  in  the  inclination  oi  x  g  reaches  the  stud  on 
the  extractor. 

To  close  the  Piece. 

The  rotation  of  the  levers  is  reversed.  The  beveling  of 
the  front  face  of  the  block  facilitates  the  insertion  of  the 
cartridge,  as  in  the  mountain  gun. 


24  XXIX. — CANNON    WITHOUT    RECOIL. 

To  lock  the  Breech. 

The  weight  of  the  block  tends  to  keep  the  piece  closed, 
since  the  vertical  through  s  passes  in  front  of  the  center  of 
the  crank  shaft. 

In  recoil,  the  moment  of  the  upper  lever  also  tends  to 
tighten  the  joint 

THE    NORDENFELT    R.    F.    GUN.      FIGURES     26,  27,  28. 

This  is  principally  intended  to  overcome  an  objection  to 
the  Hotchkiss  system,  that  is  based  upon  the  guillotining 
action  of  its  block,  in  case  the  cartridge  is  not  fully  inserted 
into  the  chamber  before  the  breech  is  closed. 

Its  operation  resembles  that  of  the  Hotchkiss,  but  in  its 
construction  the  breech-block  is  divided  by  a  plane  of  right 
section  into  the  block  proper,  B,  in  front;  and  the  wedge, 
W,  in  rear. 

The  upper  rear  porti6n  of  the  wedge  forms  a  convex 
cylindrical  surface  with  its  elements  at  right  angles  to  the 
axis  of  the  bore. 

The  first  motion  in  opening  the  breech  gives  a  downward 
movement  to  the  wedge,  the  block  remaining  at  rest.  As  the 
hand  lever  continues  to  move,  the  block  and  wedge  revolve 
downward  and  backward  together,  so  that  when,  as  in  clos- 
ing, these  motions  are  reversed,  the  cartridge  is  pressed 
home.  This  arrangement  permits  the  cartridge  to  be  actually 


Note: — Observe  \h^  face  plate,  fp,  and  the  detachable  hammer  point 
both  good  examples  of  independence  of  function. 

The  breech-block  may  be  dismounted  by  opening  the  gun  after 
removing  the  stop-screw.  In  this  case  the  crank  is  revolved  downward 
into  a  cavity  formed  for  this  purpose  on  the  right  face  of  the  breech-block. 
The  crank  may  be  turned  so  as  to  emerge  to  the  front  from  the  groove; 
the  block,  being  no  longer  supported  on  the  stud,  will  then  drop. 


XXIX. — CANNON    WITHOUT    RECOIL.  25 

thrown  into  place,  as  its  base  may  rebound  several  inches 
without  affecting  the  rapidity  of  fire. 

MAXIM    R.    F.    GUN.      FIGURES  29,  30,  31,  32. 

Nomenclature. 

The  breech-block  C,  slides  vertically  in  the  barrel,  A^  and 
not  in  the  jacket,  as  is  usually  the  case. 

The  barrel  slides  back  and  forth  for  about  six  inches  in  the 
relatively  thin  jacket,  £. 

The  jacket  carries  the  trunnions,  and  beneath  it  is  attached 
the  cylinder  of  the  hydraulic  buffer,  Z>.  The  piston  rod  of 
the  buffer  is  attached  to  the  barrel  in  rear,  and  is  surrounded 
by  a  powerful  helical  spring  lying  within  the  cylinder.  This 
spring  gives  the  counter-recoil  as  in  the  smaller  model. 

Beneath  the  mouth  of  the  chamber  the  barrel  is  traversed 
by  the  rocking  shafts  K^  to  which  are  rigidly  attached  two 
curved  arms  of  which  but  one,  y,  is  shown.  The  arms  are 
united  in  rear  by  a  cross  pin,  J/",  that  plays  in  a  slot,  iV, 
passing  through  the  block. 

The  extractor,  in  one  piece,  is  composed  of  the  upper 
claw,  X,  which  engages  with  the  rim  of  the  cartridge,  and 
of  the  tail^  H.  The  extractor  revolves  about  the  horizontal 
axis,  Z,  lying  between  X,  and  H.  Its  upper  portion,  seen 
from  the  rear,  is  crescent  shaped  so  as  to  engage  both 
sides  of  the  rim  of  the  cartridge.  Each  of  the  arms  of  the 
crescent  carries  a  projection,  F,  that  may  engage  in  a  corre- 
sponding depression  in  the  upper  front  edge  of  the  block. 
Operation. 

When  the  gun  is  fired  the  barrel  and  block  recoil  together, 
with  no  relative  motion  between  them.  The  hydraulic  buffer 
acts  as  usual,  and  the  counter-recoil  spring  is  compressed. 

As  the  spring  draws  the  burel  forward,  by  means  of  some 


26  XXIX. — CANNON    WITHOUT    RECOIL. 

mechanism  in  the  side  box,  hereafter  explained,  the  rocking 
shaft  is  given  a  small  left  handed  rotation  that  causes  M  to 
slide  through  N  and  so  depress  the  block.  As  the  block 
passes  H  ii  presses  it  to  the  front,  first  extracting  and  then 
ejecting  the  cartridge  by  means  of  the  gradually  increasing 
curvature  of  H. 

At  the  same  time  the  hammer  within  the  block  is  cocked, 
and  other  necessary  functions  are  performed  by  means  not 
herein  described. 

As  soon  as  the  cartridge  has  been  ejected,  the  block  is 
raised  by  the  action  of  a  spring  which  the  act  of  recoil  has 
compressed  until  it  is  caught  by  the  projection  V,  V. 

The  entrance  to  the  chamber  being  then  clear,  (or  the  door 
held  open  by  the  latch,  AT,)  if  a  cartridge  be  inserted,  X  is 
pressed  forward  by  the  rim  of  the  cartridge  and  F  released. 
The  spring  before  mentioned  then  fully  closes  the  block. 

By  pulling  the  trigger,  T,  the  piece  may  then  be  fired  and 
the  cycle  be  repeated.  Or  if,  during  the  closing,  the  trigger 
be  kept  drawn  back,  the  piece  will  be  fired  at  the  instant 
that  the  breech  is  closed.  Under  these  circumstances  the 
operation  is  completely  automatic  except  as  concerns  the 
loading;  the  weight  of  the  ammunition  requires  this  to  be 
done  by  hand. 

A  rapidity  of  80  rounds  per  minute  has  been  attained  with 
the  3  pdrs.,  and  guns  have  been  designed  up  to  a  40  pdr. 
caliber. 

In    commencing  the  firing,    the    rocking   shaft  may   be 
revolved  enough  to  open  the  breech  by  means  of  an  in- 
dependent handle  outside.     This  may  be  also  used  when  a 
cartridge  misses  fire. 
Advantages. 

A  reduction  of  the  work  done  on  the  carriage  by  the  gun. 
A  diminution  of  the  jump,  and  of  the  vibrations,  caused  by 


XXIX. — CANNON    WITHOUT    RECOIL.  27 

operating  a  hand  lever.  The  reduction  of  the  number  of 
gunners  required.  One  man  can  fire  ten  aimed  rounds  per 
minute,  and  can  deliver  unaimed  fire  as  rapidly  as  he  can 
throw  the  cartridges  into  the  chamber. 

The  increase  in  efficiency  of  service  due  to  the  greater  safety 
and  certainty  of  operation,  and  the  increased  accuracy  of 
this  arm,  compensate  for  its  slightly  greater  complexity  of 
structure  as  compared  with  other  hand  loaded  Rapid  Fire 
Guub. 

Side  Box. 

As  the  barrel  recoils,  the  shaft,  K^  figure  31,  goes  with  it, 
carrying  the  triangular  piece  shown,  upon  the  lower  corner 
of  which  is  the  friction  roller  e. 

The  upper  end  at  a  slides  under  the  lever,  <:,  which  is  kept 
in  close  contact  with  a  by  the  spring  d. 

When  the  counter  recoil  spring  in  D  draws  K  forward,  the 
notch  in  a  engages  with  the  rear  end  of  c.  This  tilts  the 
triangular  piece  into  the  position  shown  in  figure  82 ;  the 
spring,  b^  being  compressed  by  the  rising  of  the  roller,  e. 

The  partial  rotation  thus  given  to  K  causes  the  breech- 
block to  descend  as  before  explained. 

The  block  is  kept  from  rising  under  the  pressure  of  b^ 
until  the  projections  F",  F,  figure  29,  are  unlatched.  When  this 
occurs  the  side  mechanism  resumes  the  position  of  figure  31. 

Lock,  etc. 

As  y,  figure  29,  swings  downward,  a  cross  pin,  J/",  carries 
the  swinging  lever,  6^,  to  the  rear.  In  the  first  part  of  the 
motion  of  M  (the  slot,  N^  being  for  a  short  distance  con- 
centric with  K,^)  the  block  does  not  descend.  It  is  during 
this  time  that  G  withdraws  the  hammer,  E^  through  which  it 

*  See  page  3. 


28  XXIX. — CA^fNON   WITHOUT   kECOlL. 

passes,  sufficiently  to  allow  a  spiral  spring  surrounding  the 
firing  pin,  R^  to  retract  its  point  sufficiently  to  clear  the  front 
face  of  the  mortise  in  which  works  the  block. 

The  continued  motion  of  G  compresses  the  mainspring,  Z, 
until  the  lower  end  of  G  engages  with  the  hook  on  the  end 
of  the  firing  sear  /.  A  projection,  O^  on  G^  also  engages 
with  the  notch,  P^  in  rear  of  the  safety  sear,  F.  During  the 
closing  of  the  block  the  lever,  G,  is  thus  held  back  by  two 
sears :  figure  30. 

When  the  block  is  fully  closed  M  strikes  the  front  end  of 
F  from  below,  and  releases  O  from  P.  By  pulling  the 
trigger,  g^  figure  30,  /is  depressed  and  the  gun  is  fired. 

The  safety  sear  is  intended  to  prevent  a  premature  discharge 
when  the  trigger  is  kept  drawn  back  during  loading.  See 
page  26. 


XXX. — ACCURACY    OF    FIRE. 


CHAPTER  XXX. 
ACCURACY  OF   FIRE 

INCLUDING    pointing;    ACCURACY;    PROBABILITY   AND 
MANAGEMENT    OF   FIRE. 


I  I.  POINTING. 

To  point  a  gun  is  to  give  it  such  direction  and  elevation 
that  when  fired  the  projectile  shall  strike  a  given  target. 
The  target  may,  or  may  not  be  seen,  and  the  subject  there- 
fore divides  itself  into  direct^  and  indirect  pointing. 

DIRECT    POINTING. 

Principles. 

Remembering  that  the  line  of  sight  is  fixed  by  the  position 
of  the  target  and  the  eye,  and  includes  the  front  sight  point, 
the  object  of  the  rear  sight  is  to  determine  the  extent  to 
which  the  breech  must  be  depressed  below  the  line  of  sight 
so  as  to  give  the  angle  of  elevation  required. 

The  rear  sight  is  then  a  tangent  scale,  that  may  be  gradu- 
ated in  ranges  or  in  degrees  according  as  the  conditions  of 
loading  are,  or  are  not,  fixed. 

The  graduated  portion,  or  standard^  is  parallel  to,  and 
generally  out  of  the  plane  of  fire  at  a  distance  from  the  axis 
determined  by  the  position  of  the  front  sight. 


XXX. — ACCURACY    OF    FIRE. 


Upon  the  standard  moves  the  slide;  this  carries  the  rear 
sight  point  to  which  lateral  motion  in  both  directions  may 
be  given. 

It  is  well  to  bear  in  mind  that  the  deviation  follows  the 
motion  of  the  rear  sight  .point;  thus,  if  we  move  it  up  further 
than  is  required,  the  projectile  will  strike  high;  if  we  move 
it  too  far  to  the  right,  the  projectile  will  go  to  the  same  side 
of  the  plane  of  sight. 
Horizontal  Inclination. 

Since  the  piece  is  elevated  to  correct  for  the  action  of 
gravity,  the  elevation  must  be  taken  in  a  vertical  plane;  so 
that  if  the  trunnions  be  not  horizontal  the  rear  sight  standard 
must  be  capable  of  being  revolved  to  a  vertical  position. 

It  is  also  necessary  that  the  axis  about  which  the  rear 
sight  revolves  shall  be  the  nahiral  line  of  sight,  or  that  for 
which  the  elevation  is  0.  For  then,  since  the  natural  line 
of  sight  is  parallel  to  the  axis  of  the  piece,  the  inclination 
of  the  trunnions  will  cause  it  to  describe  a  cylindrical  sur- 
face, the  inclination  of  any  one  of  the  elements  of  which  is 
that  of  the  axis.  With  a  rear  sight  so  arranged  we  may 
measure  the  vertical  angle  included  between  the  natural  line 
of  sight  and  the  actual  or  artificial  line  of  sight,  which  is  the 
angle  required.  Thus  ni  figure  1,  if  the  trunnions  are 
inclined  at  the  angle  (]p,  the  construction  shows  that  if  the 
front  and  rear  sight  points  are  /  and  r,  the  plane  of  sight,  S^3^^ 
will  be  inclined  to  the  plane  of  fire  at  the  angle  p  f  r' :  and 
therefore,  since  the  direction  given  to  the  gun  is  fixed  by  the 
line  of  sight,  the  gun  will  shoot  to  the  left  of  the  target. 
Also,  when  the  rear  sight  is  used,  if  h  be  the  height  of  the 
slide,  the  vertical  angle  of  elevation  will  be  that  subtended 
by  only  h  cos  qp,  or  the  gun  will  shoot  low. 

But  if  the  height  of  the  front  sight  =/,  ^/,  or  the  dispart, 
(Chapter  I)  the   planes   of  sight  and   of  fire   will   become 


XXX. — ACCURACY   OF    FIRE. 


parallel ;  and  if  the  standard  be  revolved  to  a  vertical  posi- 
tion the  adjustment  will  be  complete. 

Field  Sight. 

As  a  type  of  this  class  of  sights,  that  adopted  for  the  3.2 
inch  field  gun  is  here  described. 

The  tangent  scale,  A,  figure  2  is  divided  into  degrees  and 
ten  minute  intervals;  and,  by  means  of  the  attached  vernier, 
Vj  it  may  be  read  to  minutes.  The  vernier  slide,  S,  carrying 
Xhtpeep  sight,  is  moved  to  the  desired  elevation  by  the  screw, 
E.  The  tangent  scale  admits  of  rotation  about  C,  and  may 
be  placed  in  a  vertical  plane  by  observing  the  small  spirit 
level  Z.  It  may  also  be  moved  laterally,  by  means  of  the 
screw,  W,  the  scale,  D,  indicating  the  distance  to  the  right 
or  left  of  the  natural  line  of  sight  passing  through  C. 
Sights  for  Heavy  Guns. 

When  the  axis  of  the  trunnions  is  maintained  horizontal, 
as  in  the  Siege  and  Sea  Coast  services,  the  operation  of  ele- 
vating the  piece  carries  the  natural  line  of  sight  in  a  plane 
parallel  to  the  plane  of  fire,  and  the  device  described  is  not 
required. 

For  such  pieces  the  standard  may  be  replaced  by  gradu- 
ated arcs  and  pointers  for  giving  direction  in  both  elevation 
and  azimuth.  For  the  former  purpose  the  arc  may  be  on 
the  breech  of  the  piece  or  on  the  cheek;  and  for  the  latter 
it  may  be  concentric  with  the  pintle.  The  horizontal  arc  is 
used  for  firing  at  objects  not  seen  from  the  battery;  but  the 
bearing  of  which  with  reference  to  some  meridian  is  known 
to  an  observer  outside. 
Ilelinemeiits. 

Accuracy  of  pointing  may  be  increased  by  the  use  of  tele* 


XXX. — ACCURACY    OF    FIRE. 


scopes  or  of  combined  ''peep  sights"  and  cross  wires.  To 
avoid  the  delay  in  pointing  resulting  from  the  limited  field 
of  view  a  preliminary  adjustment  with  the  ordinary  form  of 
open  sight  is  required. 

Telescopic  Sight. — This  consists  essentially  of  a  small 
transit  which  for  heavy  cannon  is  mounted  on  a  shelf  fixed 
to  one  of  the  trunnions  so  that  its  upper  plane  shall  be  paral- 
lel to  that  made  by  the  axis  of  the  bore  and  that  of  the 
trunnions.  The  telescope  is  removed  before  firing.  For 
field  guns  various  models  have  been  tried  experimentally; 
but  so  far  none  has  been  found  sufficiently  simple  for  general 
adoption.* 

Peep  Sight. — In  the  3.2  field  rifle  the  front  sight  is  as 
shown  in  figure  3,  and  the  slide  of  the  rear  sight  as  in  figure  2. 
The  distance  a  a'  is  equal  to  bb\  so  that,  having  found  the 
object  by  the  sights  a  b,  the  aim  may  be  corrected  by  the 
line  passing  through  the  peep  hole  b'  and  the  cross  wires  a' 
contained  in  the  cylindrical  housing  C. 

INDIRECT    POINTING. 

This  term  applies  to  the  method  followed  when  the  target 
cannot  be  seen  from  the  piece.  An  example  occurs  in  mortar 
practice. 

I.  The  general  practice  consists  in  establishing  an  auxil- 
iary mark  (in  mortar  practice  this  is  the  front  plummet)  to- 
wards which  the  piece  is  pointed.     The  elevation  is  subse- 


*  A  simple  form  of  telescopic  sight  for  the  field  gun  is  now,  1890, 
under  trial. 

The  vernier  slide,  S,  is  extended  to  the  left  as  shown  in  figure  2,  so 
as  to  form  one  support  for  a  telescope,  the  other  end  of  which  rests  on  a 
similar  crutch  near  the  right  trunnion. 

When  detached,  the  telescope  may  be  used  for  watching  the  effect  of 
the  fire. 


XXX. — ACCURACY   OF   FIRK. 


quently  given  by  the  level  and  corrected  by  an  observer  so 
situated  as  to  see  the  effect  of  the  fire. 

II.  Or  else,  the  proper  elevation  of  the  piece  having  been 
determined  by  trial,  a  distant  mark  may  be  selected  (or 
placed)  in  the  plane  of  sight;  the  slide  of  the  rear  sight  may 
then  be  moved  until  the  rear  sight  point  is  on  the  prolon- 
gation of  the  line  joining  the  mark  and  the  front  sight  point. 
Whenever  then,  after  firing,  the  new  line  of  sight  passes 
through  the  mark,  the  piece  will  have  its  primitive  direction 
and  elevajtion,  provided  that  its  new  position  does  not  differ 
materially  from  its  primitive  position.  This  method  is  service- 
able in  small  arm  firing. 

'  III.  In  some  cases  it  may  not  be  possible  to  find  a  suitable 
mark.  Under  such  circumstances  the  following  method  may 
be  employed  with  cannon  mounted  on  permanent  platforms. 
Establish  nearly  parallel  to  the  axis  of  the  piece,  when  in  its 
normal  position,  a  vertical  plane  director.  Establish  by  trial 
the  piece  in  its  proper  direction  and  measure  the  shortest 
distance;  1st,  from  the  plane  director  to  the  end  of  the 
axle  arm;  and  2nd,  from  the  plane  director  to  some  definite 
point  on  the  trail.  When,  after  firing,  these  distances  are 
restored,  the  piece  is  in  its  primitive  direction. 

By  establishing  the  inclination  of  the  plane  directoE  with 
reference  to  some  common  meridian,  this  method  enables 
any  piece  of  a  battery  to  be  oriented  on  the  target  by  a 
distant  observer  in  the  manner  indicated  page  3. 

Tables  provided  for  this  purpose  give  the  difference  of 
distance  from  the  plane  director  for  all  inclinations  to  the 
common  meridian  likely  to  occur  in  practice. 

II.   ACCURACY  OF  FIRE. 
Definitions. 

The  plane  curve  discussed  in  Chapter  XX  is  called  the 
normal  trajectory.     In  practice  the  trajectory  is  a  curve  of 


XXX. — ACCURACY    OF    FIRE. 


double  curvature.  The  conditions  of  firing  vary  so  greatly 
that  it  is  impossible  to  secure  the  coincidence  of  two  con- 
secutive trajectories,  so  that,  however  constant  these  con- 
ditions may  be  made,  the  trajectories  of  any  series  of  shots 
group  themselves  in  the  sheaf  of  trajectories^  a  sort  of  bent 
cone,  the  apex  of  which  is  at  the  muzzle  and  the  axis  of 
which  is  the  inean  trajectory.     Figure  34, 

Owing  to  the  tendency  of  the  individual  trajectories  to 
approach  the  mean  trajectory,  the  density  of  the  sheaf  in- 
creases toward  its  axis,  like  the  stream  from  a  hose.  Figure 
33  shows  approximately  the  manner  in  which  the  sheaf  is 
subdivided:  the  nucleus  v.ox\\.2^\n'i  the  half  lying  nearest  to  the 
axis;  the  ejivelope  surrounds  the  nucleus  and  contains  40  per 
cent  of  the  whole,  and  the  remaining  10  per  cent  constitute 
lh£  tailings. 

In  order  to  hit  the  target  we  must  know  its  position  with 
reference  to  the  mean  trajectory,  or  the  deviation  of  the  gun 
at  the  range  in  question,  and  also  the  distribution  of  the 
trajectories  throughout  the  sheaf,  or  the  errors.  We  may 
accordingly  study  1st,  the  causes  of  deviation  and  the  cor- 
rections required  to  make  the  mean  trajectory  pass  through 
the  target;  and  2nd,  the  measurement  of  the  errors  of  the 
systenj  comprising  the  gun,  ammunition,  carriage,  gunner, 
etc.,  with  a  view  of  estimating  the  probability  of  striking  a 
target  of  known  dimensions  at  a  given  range. 

I.   CAUSES  OF  DEVIATION. 

These  may  be  either  internal  or  external,  as  follows: — 

Internal. 

These  are  variations  in  the  conditions  of  loading,  in  the 
temperature  of  the  bore  and  in  meteorological  conditions. 
They  affect  the  Initial  Velocity,  and  for  practical  purposes 


XXX. — ACCURACY    OF    FIRE. 


may  be  neglected,  since  the  variations  in  velocity  may  be 

made  less  than  1  per  cent. 

External. 

Among  the  external  causes  leading  to  deviation  are: — 

I.  The  error  of  the  eye. 

II.  The  drift,  due  to  the  rotation  of  the  projectile.  See 
Chapter  XX. 

III.  The  wind  and  weather. 

IV.  The  inclination  of  the  trunnions  to  the  horizon,  and 
the  jump. 

V.  Errors  in  estimating  the  distance  to  the  target,  and 
also  those  due  to  variations  in  the  angle  of  sight,  or  in  the 
difference  of  level  between  the  gun  and  the  object. 

VI.  The  rotation  of  the  earth.  This  has  no  practical 
importance  and  may  be  neglected.  In  the  northern  hemis- 
phere it  carries  the  projectile  to  the  right  of  the  object. 

These  causes  and  their  corrections  are  discussed  as 
follows: — 

I.   The  Error  of  the  Eye. 

The  average  error  of  the  eye  among  a  number  of  selected 
marksmen,  determined  by  the  method  jLised  in  the  prelimi- 
nary instruction  in  small  arms  firing,  is  such  that  only  about 
one  half  can  be  depended  on  to  direct  the  line  of  sight  in- 
variably upon  a  2  foot  target  at  1000  yards. 

This  error  arises  principally  from  variations  in  the  height 
at  which  the  line  of  sight  pierces  the  front  sight  of  the  piece. 
It  may  be  diminished  by  increasmg  the  sight  radios,  by  the 
use  of  telescopes  and  cross  hairs,  and  by  allowing  for  vari- 
ations in  the  illumination  of  the  front  sight.  When  the  front 
sight  is  obscured,  too  much  of  it  will  be  taken,  and  when 
one  side  is  brighter  than  the  other  the  deviation  will  be  from 
the  light. 


XXX. — ACCURACY    OF    FIRE. 


The  nearer  is  the  eye  to  the  rear  sight,  the  better  will  the 
front  sight  be  seen,  and  the  ^ner  can  the  sight  be  taken. 

The  permissible  error  of  the  eye  will  depend  upon  the 
semi-height  of  the  target  and  its  distance;  or,  calling  e  the 
error,  /  the  sig/i^  radius  of  the  gun,  R  the  range,  and  h  the 
height  of  the  target,  we  have,  assuming  from  the  principle 
of  rigidity  of  the  trajectory  that  it  is  a  straight  line,  and 
from  the  similarity  of  the  triangles  in  figure  4, 
h       ^  hi 


:/::-  \  R  oi  e 


2   '  2R' 

II.   Drift. 

As  the  elevation  increases,  the  deviation  due  to  drift 
increases  more  rapidly  than  the  range,  so  that  the  horizontal 
projection  of  the  mean  trajectory  is  convex  toward  the  plane 
of  fire. 

Drift  may  be  approximately  compensated  by  giving  to  the 
rear  sight  leaf  a  permanent  inclination  to  the  plane  of  fire 
in  the  direction  opposed  to  the  drift.  The  angle  of  incli- 
nation is  called  the  J^ermanent  angle.     It  may  be  shown  that 

D 

tan  t  =  -^—. — . 
R  sm  g 

in  which  i  h  the  permanent  angle;  Z>,  the  deviation  due  to 
drift;  R,  the  range,  and  e  the  angle  of  elevation. 

Sin  e  increases  more  rapidly  than  the  range,  so  that  if  D 
varied  as  R  sin  e,  i  would  be  constant. 

Drift  at  ordinary  ranges  may  be  sufficiently  compensated 
for  by  the  permanent  angle,  and  at  long  ranges  a  further 
correction  may  be  given  by  the  lateral  motion  of  the  rear 
sight  slide. 

With  pointed  projectiles  the  drift  is  in  the  direction  of  the 
rifling.     In  the  U.  S.  service  this  is  to  the  right. 

Range  tables,  giving  the  ballistic  properties  of  the  gun  as 
determined  by  experiment,  furnish  the  angles  of  elevation 


XXX. — ACCURACY    OF    FIRE. 


and  the  drift  for  the  different  ranges  as  well  as  the  perma- 
nent angle. 

RANGE  TABLE  FROM  EXPERIMENT. 

English  8  in.  M.  L.  R.  Howitzer  (»)— («^=180  lbs.),  w  of  R.  L.  G3. 


1 

is 

5'  chanj^e  of 

e  or  d 
changes.  (») 

50  per  cent. 
zonesi=2/'.(^) 

/.  F. 

X 

e. 

drift 

1.^ 

GO. 

V. 

T. 

!» 

w 

X, 

F.orZ, 

x{*) 

y- 

Z. 

1 

lbs. 

f.s. 

yds. 

0/ 

yds. 

0/ 

0/ 

yds. 

yds. 

yds. 

yds.'  yds. 

f.s. 

sec. 

1 

1200 

2.44 

1.9 

0.06 

4.00 

25.0 

1.74 

16.4 

0.40    1.21 

876 

4.0 

1600 

5.06 

3.8 

0.09 

5.36 

23.8 

2.32 

21.3 

0.56 i  2.14 

852 

5.4 

11.5 

956  [ 

2300 

7.3;^ 

8.7 

0.13 

8.42 

23.8 

3.34 

29.7 

0.87  i  4.64 

814 

7.9 

3400 

7.54 

9.5 

0.13 

9.12 

22.7 

3.49 

30.9 

0.92!  5.07 

809 

8.2 

J 

2600 

8.16 

10.4 

0.14 

9.42 

22.7 

3.63 

32.1 

0.98|  5.50 

804 

8.6 

1 

1200 

4.12 

2.3 

0.07 

4.36 

20.8 

1.74 

15.5 

0.45    1.31 

845 

4.1 

1600 

5.4K 

4.5 

0.10 

6.21 

20.8 

2.32 

20.3 

0.62'  2.31 

823 

5.6 

10.5 

920  I 

2300 

8.36 

10.5 

0.16 

9..51 

20.8 

3.34 

28.3 

0.99    4.99 

787 

8.3 

2400 

9.00 

11.5 

0.17 

10.24 

20.8 

3.49 

29.4 

1.05 1  5.44 

782 

8.7 

J 

2500 

9.24 

12.7 

0.18 

10.57 

20.2 

3.63 

30.5 

1.12    5.90 

777 

9.1 

473} 

1200 

ifi.as 

11.4 

0.33 

17.30 

4.6 

1.74 

21.7 

1.50    6.9 

438 

8.4 

3.5 

1600 

24.21 

22.3 

0.48 

26.00 

3.6 

2.32 

30.4 

2.18  14.9 

433 

11.8 

1. 

2. 

3. 

4. 

5. 

6. 

7. 

8. 

9. 

10. 

11. 

12. 

13. 

14. 

III.   The  Wind. 

For  any  range  the  deviation  of  a  projectile  caused  by  a 
wind  of  which  the  velocity  is  one  mile  per  hour,  acting  at 


(1)  The  rear  sight  of  this  piece  is  not  set  at  the  permanent  angle. 
(»)  The  actual  time  of  burning  varies  in  flight  from  that  at  rest.    See  Chapter 
XVm,  page  7. 

(3)  Eange  tables  for  guns  assume  a  constant  value  of  w.    They  give  in  addition 

to  the  above,  the  jump,  the  inclination  of  qo  as    —,  and  the  penetration  in  wrought 
iron  at  the  different  ranges. 

(*)  For  guns  this  is  much  more  uniform.  See  page  52. 

(■)  See  post. 


10  XXX. ACCURACY    OF    FIRE. 

right  angles  to  the  plane  of  fire,  is  called  the  coefficient  of 
the  deviation  for  that  range.  So  that,  calling  u  the  velocity 
of  the  wind  in  miles  per  hour  as  shown  by  the  anenometer, 
^  the  inclination  of  the  wind  to  the  plane  of  fire  as  shown 
by  the  wind  vane,  and  k  the  coefficient  above  defined,  we 
have 

D  ^ku  sin  ^. 
The  relation  between  k  and  R  may  be  recorded  by  an  em- 
pirical curve,  from  the  indications  of  which  the  rear  sight 
may  be  set  to  the  right  or  left  of  its  normal  position  when 
the  force  and  the  direction  of  the  wind  are  known. 
The  Weather. 

The  relative  effect  of  varying  meteorological  conditions 
is  provided  for  by  the  coefficients  explained  in  Chapter  XX, 
pp.  9,  11. 
IV.  Inclination  of  the  Trunnions. 

This  has  been  explained  page  2. 

V.   ESTIMATION  OF  DISTANCES.* 

The  importance  of  this  correction  varies  inversely  with 
the  height  of  the  target  and  the  flatness  of  the  trajectory. 
Chapter  XX,  Eq.  (30). 

The  distance  of  the  target  may  be  ascertained: — 

1st.  By  the  eye. 

Constant  practice  is  necessary,  even  at  short  ranges,  and 
the  results  are  much  affected  by  varying  atmospheric  con- 
ditions and  by  the  nature  of  the  intervening  ground.  At 
long  ranges  it  even  requires  experience  to  determine  whether 
a  shell  bursts  short  or  beyond  the  target. 

2nd.  By  rapid  measurements  with  different  range  finder  s.\ 

*  The  extent  of  this  sub-head  requires  a  variation  in  the  method  of 
using  type.     The  subject  extends  to  page  22. 
\  For  3rd  see  page  21. 


XXX. — ACCURACY    OF    FIRE.  11 


RANGE  FINDERS  OR  TELEMETERS. 

These  may  be  divided  into  two  general  classes,  the  acoustic 
and  the  optical  instruments.  The  former  depend  upon  the 
assumed  constancy  of  the  velocity  of  sound,  and  the  latter 
upon  the  rapid  solution  of  plane  triangles. 

1.     ACOUSTIC    TELEMETERS. 

These  measure  the  time  elapsing  between  the  flash  of  an 
enemy's  gun  and  the  arrival  of  the  report.  Then,  taking 
tiie  velocity  of  sound  at  1100  f.  s.  we  have  R=.vt,  The 
following  methods  are  in  use. 

1.   The  Le  Boulenge  Telemeter. 

This  consists  of  a  graduated  glass  tube  filled  with  some 
non-freezing  transparent  liquid,  through  which,  when  the 
tube  is  vertical,  a  metallic  index  falls  with  a  slow  uniform 
motion. 

To  use  the  instrument,  hold  it  horizontally  with  the  index 
at  0:  the  instant  that  the  flash  or  smoke  is  seen  turn  it  ver- 
tical; when  the  sound  is  heard  return  the  tube  to  a  hori- 
zontal position  and  take  the  reading  in  meters. 

2.  A  simple  method  is  to  count  the  number,  «,  of  cadenced 

steps  made  during  this  interval.     If  these  are  at  the  rate  of 

110  per  minute,  then 

1100x60       ^_^ 
R  in  yards  =  n  -— — — -r-  =  200  n. 

o  X  ilU 
2.    OPTICAL    TELEMETERS. 

General  Principles. 

If  we  consider  the  distant  object  as  a  point,  its  parallax 
is  the  apparent  difference  of  direction  of  the  object  as  seen 
from  two  different  points  of  view;  and  conversely,  if  the 
dimensions  of  the  object  are  considerable,  its  parallax  may 


12  XXX. — ACCURACY    OF    FIRE. 

be  measured  by  the  angle  that  it  subtends  from  a  single 
point  of  view. 

The  triangle  formed  in  the  first  instance  by  the  object 
and  the  two  points  of  view,  and  in  the  second  case  by  the 
point  of  view  and  the  observed  extremities  of  the  object  is 
the  triangle  to  be  solved.  Its  solution  is  facilitated  and 
sufficient  accuracy  for  first  approximations  attained  by  con- 
sidering it  either  a  right  angled  triangle  or  an  isoceles 
triangle,  of  which,  in  the  first  case  the  distance  between  the 
two  points  of  view,  and  in  the  second  case  the  known  or 
assumed  dimensions  of  the  object  forms  the  base.  The  base 
or  the  point  of  view  should  evidently  be  selected  so  as  to 
diminish  the  error  of  this  assumption. 

If  the  triangle  to  be  solved  is  a  right  angled  triangle, 
figure  5,  we  may  measure  ^  C  by  multiplying  the  length  of 
the  base  ^^  by  the  reciprocal  of  the  sine  of  the  parallax 
at  C  when  this  is  found;  or,  as  the  parallax  is  generally 
small,  the  reciprocal  of  the  tangent  may  be  used,  giving  CB 
practically  equal  to  A  C,  figure  6. 

If  the  triangle  is  isoceles  the  length  of  a  side  will  be  given 

A  B  ] 

by  X  —. — ;;.     Some  instruments  use  a  fixed   parallax 

•'      2         sm  I" 

and  vary  the  position  of  the  observer  at  the  extremities  of 
the  base  until  the  desired  triangle  is  formed.    As  the  paral- 
lax is  so  chosen  that  -: — r  is  a  whole  number,  say  20,  it  is 
sm§ 

only  necessary  to  multiply  the  length  of  the  base  by  10  to 
obtain  the  range.     This  can  easily  be  done  mentally. 
Classiiication. 

Accordingly  instruments  may  be  classified  as  follows;-— 

I.  Fixed  base,  variable  parallax. 

II.  Fixed  parallax,  variable  base. 

III.  Variable  parallax,  variable  base. 


XXX. — ACCURACY   OF   FIRE.  Vd 

The  same  instrument  may  sometimes  be  used  in  more 
than  one  method,  and  the  parallax  may  be  either  vertical  or 
horizontal. 

In  Older  to  diminish  their  size  and  to  permit  the  simulta- 
neous observation  of  two  distant  points  from  an  unsteady 
support,  many  instruments  employ  the  principle  of  the  sex- 
tant by  using  two  reflecting  surfaces,  the  angle  between 
which  is  one  half  of  that  between  the  incident  and  the  second 
reflected  ray,  figure  7.  The  relative  inclination  of  the 
reflecting  surfaces  m^  m^  may  be  fixed,  or,  as  in  the  sextant, 
variable. 

The  conflicting  claims  of  portability,  rapidity  of  operation 
and  accuracy  have  caused  many  forms  of  range  finders  to 
be  devised.     No  one  kind  has  yet  been  generally  adopted. 

The  ingenuity  of  inventors  has  been  principally  exercised 
in  increasing  the  scale  on  which  the  parallax  is  measured 
and  in  avoiding  all  but  the  simplest  computations  in  the  field. 
Vertical  Parallax. 

These  instruments  require  the  vertical  base  to  be  known. 
The  base  may  be,  1,  either  the  height  of  the  object,  as  the 
average  height  of  a  man,  or  that  of  the  mast  or  funnel  of  an 
enemy's  vessel,  or,  2,  the  height  of  the  instrument  above  the 
horizontal  plane  on  which  the  object  is  situated,  as  in  coast 
batteries  having  considerable  command. 
1.   Stadfa.     Figure  8. 

This  instrument  was  formerly  used  when  the  ranges  of 
small  arms  were  so  short  that  the  parallax  for  an  object  the 
height  of  a  man  was  of  appreciable  magnitude. 

The  button  b  is  held  between  the  teeth,  and  the  Stadia  S 
is  held  at  a  distance  from  the  eye  regulated  by  the  cord  c. 
The  head  and  feet  of  the  man  whose  distance  is  to  be 
measured  are  brought  tangent  to  the  lines  oh^  ot,  and  the 
slide  *S'  brought  to  the  corresponding  position  along  the 


14  XXX. — ACCURACY   OF   FIRE. 

scale.  The  average  height  of  a  man  in  this  service  is  taken 
at  5  ft.  8  in. 

The  objections  to  this  particular  instrument  are  evident, 
but  the  principle  is  applicable  against  vessels.  A  very  con- 
venient surveying  instrument  of  this  nature  uses  fixed  paral- 
lel horizontal  wires  inside  a  telescope,  and  a  graduated  staff, 
from  which  the  distance  to  the  staff  may  be  read  off  directly. 
2.   The  Depression  Range  Finder. 

This  consists  of  a  telescope,  the  height  of  which  above 
the  water  level  is  known.  The  distance  and  direction  of  the 
object  can  be  read  directly  from  scales;  so  that,  if  the  ob- 
server be  remote  from  the  smoke  of  the  battery,  and  be 
screened  by  natural  objects  from  the  enemy's  view,  he  may 
safely  direct  the  continuous  firing  of  pieces  provided  with 
the  pointing  apparatus  described  page  3. 

The  instrument  admits  of  a  correction  for  the  stage  of 
tide,  etc. 

HORIZONTAL  PARALLAX. 

CLASS   I.       FIXED    base;    VARIABLE    PARALLAX. 

1.   The  Plane  Table. 

This  is  used  in  plotting  the  effects  of  fire  over  water,  and 
the  principle  is  applicable  in  warfare. 

For  target  practice  the  base  is  established  so  that  straight 
lines  drawn  from  its  extremities  to  the  point  of  impact  shall 
intersect  as  nearly  as  possible  at  right  angles.  The  position 
of  the  base  with  reference  to  the  piece  having  been  estab- 
lished on  a  chart,  the  various  points  of  fall  can  be  plotted 
in  their  relative  positions  and  the  ranges  and  deviations 
determined  by  a  scale.  In  this  practice  the  base  may  be 
established  parallel  to  the  plane  of  fire  and  near  the  target; 
but  as  in  war  this  would  not  be  possible,  the  equivalent  of 


XXX. — ACCURACY    OF    FIRE.  15 

the  plane  table  is  established  so  near  the  piece  that  the 
difference  of  its  distance  from  the  object  may  be  neglected. 
In  such  cases  the  length  of  the  base  should  increase  with 
the  range,  so  as  to  neutralize  errors  in  observing  the  paral- 
lax; but  since  in  practice  a  base  of  suitable  length  cannot 
always  be  obtained,  the  errors  due  to  the  use  of  a  short  base 
may  be  corrected  by  refinements  in  the  construction  of  the 
instrument,  as  in  the  following  cases. 

2.  Berdan  Range  Finder.     Figure  9. 

In  this  instrument  we  find  a  fixed  base  only  6  feet  long, 
so  that  it  is  contained  within  .the  limits  of  the  vehicle  on 
which  the  whole  apparatus  is  carried.  At  one  end  is  the 
fixed  telescope  B  with  its  line  of  collimation  exactly  at 
right  angles  to  the  base  A  B.  The  inclination  of  the  mova- 
ble telescope  A  to  the  axis  of  B^  or  the  parallax  of  the  ob- 
ject C,  can  be  read  off  from  a  scale  giving  A  C  directly. 
This  instrument  is  rapid  and  accurate;  but  is  necessarily 
confined  to  the  Artillery. 

3.  The  Fiske  Range  Finder.     Figure  10. 

This  is  intended  to  be  used  on  naval  vessels  in  which  the 
length  of  the  base  is  necessarily  restricted.  It  operates  on 
the  same  general  principle  as  the  Berdan;  but  permits  the 
solution  of  oblique  angled  triangles.  In  order  to  magnify 
the  scale  it  employs  the  principle  of  the  Wheatstone  Bridge. 

Let  A  B  \>&  the  base,  at  each  end  of  which  is  a  telescope 
pivoted  at  A  and  B^  which  are  the  centers  of  the  graduated 
arcs,  G  H  I,  J  K  L.  Let  C  be  the  object.  Draw  A  E 
parallel  to  B  C,     Then 

sm  C 
The  angle  at  B  can  be  easily  measured,  and  the  angle 


16  XXX. — ACCURACY    OF    FIRE. 

IfAI=d.^L  /K—2iXC  6^  ZT,  is  determined  substantially  as 
follows. 

Let  C,  figure  11,  be  the  target  and  A  and  B  the  metallic 
pivots  of  the  two  telescopes  connected  with  the  battery  at  L, 
and  through  the  telescopes  and  their  graduated  traverse 
circles  JDEFG,  H I  J,  with  the  galvanometer  K.  The 
letters  a,  b,  c,  d^  refer  to  the  usual  nomenclature  of  the  arms 
of  the  Wheatstone  Bridge. 

The  angle  ABC  can  be  read  off  directly  from  the  trav- 
erse circle  H I J^  and  the  angle  E  A  /^=the  parallax  may 
be  measured  in  two  ways. 

First;  Supposing  the  galvanometer  to  be  under  the  eye 
of  the  observer  at  A^  he  has  merely  to  swing  his  telescope 
until  the  galvanometer  balances.  Then,  since  a  \  b  \\  c  \  d 
the  change  in  the  angle  at  A  will  be  the  parallax,  the  range 
for  which,  corresponding  to  an  angle  A  B  €•=■  90°,  can  be 
read  off  directly  from  the  traverse  circle  and  then  be  corrected 
by  multiplying  by  sin  B,  This  correction  is  mechanically 
performed  in  the  act  of  sighting  from  A, 

Second;  Suppose  the  galvanometer  to  be  under  the  eye 
of  a  distant  observer,  as  at  the  gun,  and  let  him  be  provided 
with  means  for  determining  with  sufficient  exactness  the 
angle  A  B  C,  ox  sin  B.  The  observers  at  the  telescopes 
may  then  simply  follow  the  object  with  their  instruments  and 
the  observer  at  the  gun  may  determine  the  range  by  intro- 
ducing into  the  circuit  a  rheostat  graduated  for  ranges.* 

CLASS  II.    FIXED  PARALLAX  ;    VARIABLE  BASE. 

1.    The  Weldon  Range  Finder.   Figure  7. 

This  uses  two  small,  thin,  triangular  prisms  having  one  side 
silvered  and  the  angles  between  two  of  the  reflecting  surfaces 
=  44°  17'. 


*  This  description  is  much  abbreviated  and  omits  many  interesting 
details, 


XXX. — ACCURACY    OF    FIRE.  17 


C       1 

Therefore,  in  figure  6,  ^  =  ^  =  88**  34'  and  tangent  --  =  — 

The  instrument  requires  two  observers,  each  of  whom  holds 
the  prism  so  as  to  see  C  by  double  reflection,  and  simulta- 
neously the  eye  of  the  other  observer  by  direct  vision  over 
the  prism. 

A  single  observer  may  use  the  instrument  by  establishing 
the  direction  of  the  base  line  from  A;  marking  the  spot 
and  finding  some  spot  B  upon  the  base  line  from  which  C 
can  be  seen  by  double  reflection  and  A  by  direct  vision. 
Then 

2.   The  Pratt  Range  Finder.     Figure  12. 

Each  instrument  contains  two  pairs  of  mirrors,  called  the 
upper  and  the  lower  pair.  The  upper  pair  are  inclined  at 
45°  to  each  other,  and  the  lower  pair  at  an  angle  of  less  than 
45°.  Suppose  this  angle  to  be  fixed,  as  in  the  Weldon  at 
44°  17',  although  it  may  be  set  at  various  other  angles. 

1.  Suppose  the  distance  B  C,  figure  13,  is  to  be  measured. 
Standing  at  B,  with  the  upper  mirrors  and  by  direct  vision 
establish  some  distant  and  well  defined  mark  D,  so  taken 
that  CB D=i  90°,  and  mark  the  point  B. 

Move  in  the  prolongation  oi  D  B  till  A  is  reached,  from 
which  point  D  seen  by  direct  vision  coincides  with  the  image 
of  C  reflected  in  the  lower  pair  of  mirrors.     Then 

AB^M<i-BC. 

2.  The  operation  may  be  reversed  by  moving  from  A  to 
B.  In  this  case,  as  the  observer's  back  will  be  turned  to- 
wards A  while  changing  his  station,  the  direction  AD  should 
be  preserved  by  selecting  an  auxiliary  mark  d'  between  Z> 
and  B, 


18  XXX. — ACCURACY    OF    FIRE. 

3.  It  is  evident  that  the  instrument  may  be  used  for  solv 
ing  isoceles  triangles  in  the  same  manner  as  the  Weldon. 

4.  The  instrument  may  be  used  to  measure  the  distance 
between  two  objects,  both  of  which  are  inaccessible,  as  in 
determining  on  shore,  the  distance  between  a  friendly  vessel 
and  an  enemy's.  To  illustrate,  let  B  C,  figure  14,  be  the 
distance  to  be  measured  and  let  the  obsejrver  be  at  A.  Es- 
tablish ^  Z>  at  right  angles  \.o  A  B  and  with  the  lower  pair 

A  B 
of  mirrors  determine  the  point  D  so  that  A  D  =  -j~- .   The 

distance  A  B  need  not  be  measured. 

A  C 

Similarly,  determine  the  point  E  so  that  A  E=  -j—  , 

Then,  since  A  D  E  and  ABC  are  similar  triangles, 
BC^A:^  ED. 
Remark. 

Instruments  of  Class  II  are  simple,  portable  and  fairly 
accurate;  but  in  broken  or  wooded  country  time  may  be 
lost  in  finding  a  base  suited  to  the  parallax. 

CLASS    III.     VARIABLE    BASE;    VARIABLE    PARALLAX, 

1.   Gautier's  Telemeter. 

This  is  one  of  the  earliest  and  best  forms  of  this  class. 
Its  essential  principles  may  be  illustrated  as  follows. 

Suppose  we  have  a  form  of  protractor  such  as  the  dividers 
shown  in  figure  15,  and  provided  with  sight  points  at  ^,  b,  c. 
Let  it  be  required  to  find  the  distance  A  C,  figure  16. 

Select  some  distant  point  Z>,  such  that  CB £)=cab=z^O^, 
Then  advance  to  A  on  the  line  BD  and  sight  along  ab 
at  Cj  d  c  will  then  point  to  X>' .  If  now  we  move  a  c  ^o 
that  while  a  b  still  points  \.o  C^  ac  will  point  to  Z>,  the  change 

cac'  will  be  the  parallax  and  AC=  ABy.  -. j . 

sm  cac' 


XXX. — ACCURACY   OE   FIRE.  19 


In  practice  c ab  =  A  B  C  may  vary  8°  from  90°  without 

A  C 
causing  the  resulting  error  in  range  to  exceed——  .     This 

permits  slight  modifications  in  the  length  of  the  base  to  allow 
for  the  nature  of  the  ground. 

Construction. 

The  instrument  resembles  in  appearance  a  telescope,  the 
object  glass  being  replaced  by  a  glass  prism,  the  angle  of 
which  is  6°.  This  is  set  in  a  graduated  ring  that  may  be 
turned  axially  about  the  line  of  collimation  of  the  eye  piece  E. 

The  prism  causes  rays  entering  from  the  front  to  be  devi- 
ated by  an  amount  /  T I\  equal  to  half  the  angle  of  the 
prism,  or  3°.  So  that  by  turning  the  graduated  ring  the 
refracted  ray  will  describe  a  cone,  the  angle  of  which  is  6°. 
The  ring  is  graduated  for  the  reciprocal  of  the  sines  of  the 
intermediate  angles  corresponding  to  whole  numbers  vary- 
ing by  10,  20,  etc. 

Operation.    Figure  16. 

The  variable  inclination  of  the  mirrors  permits  the  points 
B  and  Z>Z^  to  be  selected  according  to  the  ground.  Hav- 
ing caused  the  image  of  C  in  the  mirror  M  to  come  just 
below  some  well  defined  point  of  D  seen  through  the  prism 

when  set  at  "Infinity"  or-^— - ,  we  may  then  advance  along 

B  Z>  to  A  and  restore  coincidence  by  turning  the  graduated 
ring,  the  reading  of  which  will  give  the  multiplier  for  the 
base. 

Or  else,  we  may  set  the  ring  to  some  simple  factor  as  20, 
and  advance  until  coincidence  is  made. 

Like  the  other  instruments,  the  Gautier  admits  of  a 
variety  of  applications. 


20  XXX. — ACCURACY    OF    FIRE. 

2.  The  Gordon  Range  Finder.     Figure  18. 

This  resembles  in  principle  the  Gautier.  It  consists  of  an 
opera  glass  in  front  of  which  is  mounted  a  frame  containing 
two  plane  mirrors,  MM',  M  lying  just  below  the  line  of 
collimation. 

M  may  be  turned  by  a  thumb  screw  to  an  extent  measured 
by  an  enlarged  scale,  the  0  of  graduation  of  which  corre- 
sponds to  an  inclination  of  the  mirrors  of  45°. 

Having  established  a  right  angle  at  J3,  figure  16,  we 
restore  coincidence  at  A,  and  pass  from  the  reading  to  a 
table  of  factors.  The  telescope  aids  in  defining  distant  ob- 
jects and  is  useful  in  watching  the  effects  of  the  fire,  by 
which  after  all  the  elevation  is  mainly  regulated. 

3.  The  Nolan  Range  Finder.     Figure  19. 

This  consists  of  a  pair  of  instruments,  each  of  which  com- 
prises a  tripod  upon  which  are  mounted  two  telescopes  of 
different  lengths  and  powers  and  placed  one  above  the  other 
with  their  lines  of  collimation  set  at  about  90°.  This  angle 
may  be  varied  and  the  difference  from  90°  read  from  a 
decimal  scale. 

Having  established  a  base  that  will  form  with  the  object 
nearly  an  isoceles  triangle,  we  direct  the  short  telescopes, 
s  and  /,  on  each  other,  and  the  long  telescopes,  /,  /',  on  the 
same  point  of  C.  The  sum  of  the  displacements  of  A  and  B 
is  the  parallax,  and  considering  the  triangle  isoceles, 

log  I A  C=  B  C=  -y  X  gjj^  J  )=  log  —^  +  colog  sin  |^ 

To  avoid   calculation   by   ordinary   methods    a   reckoning 

cylifider,  consisting  of  a  series   of  concentric  discs,  is  used. 

This  applies  the  principle  of  the  slide  rule  ;  since  of  two  suc- 

,,      A  B 
cessive  nngs,  one  is  graduated  in  terms  of  log— ^,    ana 


XXX. — ACCURACY    OF    FIRE.  21 


the  other  in  terms  of  colog  sin  — -.  •  By  setting  the  0  of  the 

scale  of  sines  to  the  reading  of  the  scale  of  bases,  if  we  take 
the  point  on  the  scale  of  bases  corresponding  to  the  reading 
of  the  scale  of  sines  (or  for  simplicity,  to  the  sum  of  the 
readings  on  the  two  decimal  scales)  we  have  the  range  at 
once.* 

To  avoid  having  the  tripods  to  transport,  the  instruments 
may  be  mounted  on  the  cheeks  of  the  flank  pieces  of  a 
battery. 


Returning  to  the  Estimation  of  Distances  page  10,  we 
have  as  the  next  method — 

3rd.f  By  trial  with  smaller  pieces,  using  percussion  shell, 
as  described  Chapter  XVIII,  page  12.  The  sights  for  these 
guns  should  be  graduated  in  yards. 

4th.  By  establishing  a /(?r^  by  changing  the  elevation  until 
about  one  half  of  the  projectiles  fall  short.  There  are  two 
methods  of  doing  this. 

1st.  Tht  progressive  method^  or  feeling  the  way  from  the 
first  range  by  ±  increments  until  the  target  is  en- 
closed in  the  fork. 
2nd.  The  method  of  successive  means.  Having  established 
a  large  fork  by  throwing  one  shot  short  and  one  be- 
yond the  target,  we  take  the  mean  of  the  two  ranges 
for  the  next  range;  and,  according  as  this  is  beyond 
or  short  of  the  target,  take  the  mean  of  it  and 
that  one  of  the  first  two  that  was  short  or  beyond, 

*  The  simplicity  of  this  principle  will  become  apparent  by  taking  two 
scales  of  equal  parts  'held  in  the  same  plane  and  sliding  one  along  the 
other, 
t  This  article  follows  2nd,  page  10, 


22  XXX. — ACCURACY    OF    FIRE. 

and  so  on,  continually  narrowing  the  fork.     This 
method  is  preferred  when  time  permits  its  employ- 
ment. 
In  some  services  the  number  of  turns  of  the  elevating 
screw  required  to  change  the  range  by  a  nearly  constant  in- 
crement at  the  different  ranges  is  known.      This  number 
varies  less  rapidly  than  the  range. 

Variations  in  the  Angle  of  Sight.* 

As  seen  in  Chapter  XX,  page  24,  for  the  same  elevation 
the  range  varies  somewhat  with  the  angle  of  sight.  The 
correction  for  this  with  the  flat  trajectories  now  common 
may  be  included  with  that  for  deviations  in  range. 

II.    ERRORS. 

CAUSES    OF    ERROR. 

It  is  usual  to  consider  in  gunnery  practice  that  there  are 
two  main  causes  of  error,  one  tending  to  increase  or  diminish 
the  range,  or,  what  is  the  same  thing,  tending  to  raise  or 
lower  the  trajectory,  and  producing  range  errors;  and  the 
other  tending  to  move  the  trajectory  to  the  right  or  left, 
producing  lateral  errors. 

Lateral  errors  evidently  follow  the  same  laws  as  range 
errors, 

MEASUREMENT    OF    ERRORS. 

The  errors  of  a  piece  f  at  a  given  range  are  determined 
by  firing  the  piece  under  as  constant  conditions  as  possible. 

For  small  arms  the  gun  is  clamped  in  a  fixed  rest,  and 
the  shots  received  on  an  iron  target,  the  image  of  which  is 


*  See  page  7. 

f  This  will  be  considered  to  include  the  errors  due  to  the  carriage, 
ammunition,  and  to  other  causes  of  deviation  that  cannot  be  controlled. 


XXX. — ACCURACY   OF    FIRE.  23 

projected  by  a  camera  on  a  sheet  of  paper  ruled  to  scale. 
The  target  may  then  be  computed  as  hereafter  described. 

The  resulting  accuracy  is  compared  with  that  of  alternate 
targets  made  with  a  standard  arm,  and  with  ammunition 
carefully  prepared  in  such  large  quantities  that  its  uniformity 
from,  day  to  day  may  be  considered  as  constant. 

We  may  thus  eliminate  all  variables  but  the  particular  one 
under  consideration. 

For  cannon,  however,  for  which  it  is  often  impracticable 
to  procure  vertical  targets  of  sufficient  size,  the  firing  is  often 
conducted  over  water  and  its  results  plotted  with  a  plane 
table. 

COMPUTATION. 

Definitions. 

Let  n  be  the  number  of  shots  fired.     Let  X  Y  Z  h^  the 

axes  of  coordinates,  drawn  through  the  point  aimed  at ;    }t 

being  taken  parallel  to  the  plane  of  fire,  Y  at  right  angles 

thereto,   and   Z  vertical.     Let  x' ,  x" ;  y',  y"  ;  z',  z" ;  etc., 

be  the  coordinates  of  the  shot  marks  taken  with  their  proper 

signs,  and  r' ,  r"  their  radial  distances  from  the  origin.     Let 

2"  be  the  distance  to  the  target.     Then  we  have 

it  x'  d:  x"  it  etc. 
Mean  deviatio?i  in  range,     X,  = '-, 


Mean  lateral  deviation 


Mea?t  vertical  deviation         Z,  z= 


±  y  ±  y"  ±  etc. 

71 

±  z'  ±  z"  ±  etc. 


Mea7i  range  R  z=.  T±  X , 

^  \  yji  \  r^"-L.  etc. 

Mean  radial  deviation  or  "  string'^  S  z=z -L- — -* 

?i 

Mean  point  of  impact^  or  center  of  impact.     This  is  the 

point  of  which  the  coordinates  are  (X,  FJ  or  ( Y,  Z).     This 

point  determines  the  nieaji  trajectory^  mean  line  of  fire  and 


M  XXX. — ACCURACY   OF   FIRE. 

mean  plane  of  fire.     It  is  the  center  of  the  group  of  shot 
marks,  and  the  origin  for  the  measurement  of  errorsJ^ 

Range  error  for  a  single  shot  v^  =  X,  '^  x' .  + 

Lateral  error  for  a  single  shot  v^  =   Y,  -*'  y'. 

Vertical  error  for  a  single  shot         z^g  =  Z,  ^  z'» 

Mean  error  in  range. 

Mean  lateral  error. 

Mean  vertical  error. 

Mean  absolute  error, 

n 

In  which  r^,  r^^,  etc.,  are  measured  radially  from  the  mean 
point  of  impact^  so  that 


^1 

V 

'  + 

V'  +  etc. 

n 

^2 

— 

v^ 

4- 

V  +  etc. 

n 

^3 

= 

V,' 

+ 

V  +  etc. 

?i 

^/ 

+  : 

0/  +  ^//  +  etc. 

r^=  y  v^  +  z/j,  or  =  yv.^  +  v^ 

according  to  the  position  of  the  target. 

Of  these  mean  errors  the  first  three  are  used  to  analyze 
the  causes  of  error.  Thus  if  e^  or  fg  should  be  found  to 
greatly  exceed  fg  it  would  be  assumed  that  either  the  powder, 
or  the  weight  of  the  projectile  had  varied,  or  that  there  had 
been  an  irregular  wind  in  the  direction  of  the  plane  of  fire. 
On  the  other  hand,  if  £,  should  greatly  exceed  e^  or  fg,  it 


*  While  deviations  are  measured  from  the  point  aimed  at,  errors  are 
measured  from  the  mean  point  of  impact. 

t  The  sign,  '"^,  means  that  the  coordinate  distance  between  the  mean 
point  of  impact  and  the  shot  mark  is  taken.  The  confusion  arising  when 
these  lie  on  opposite  sides  of  an  axis  may  be  avoided  by  selecting,  instead 
of  the  target,  an  arbitrary  origin  outside  the  group;  so  that  all  deviations 
shall  be  -j-. 


XXX. — ACCURACY   OF   FIRE.  25 

would  be  likely  that  there  had  been  an  irregular  wind  across 
the  plane  ot  fire. 

The  mean  absolute  error  is  principally  employed  to 
measure  the  accuracy  of  fire  arms  when  tested  under  the 
conditions  given,  page  23. 

Vertical  Projections. 

In  firing  over  water,  z',  z"  are  unknown  or  not  observed. 
Therefore,  in  order  to  determine  where  the  projectile  would 
have  passed  through  a  vertical  target  in  the  plane  KZ,  it  is 
necessary  to  assume  that  the  angle  of  fall,  w,  is  constant 
for  the  particular  range  under  consideration.  Therefore  if, 
as  in  Chapter  XX,  we  assume  that  the  trajectory  for  the 
small  distance  involved  is  a  straight  line,  we  may  write 

s  =  X  X  tan  c»,  etc. 

Similarly  if  we  assume  that  the  mean  trajectory  passes 
through  the  mean  point  of  impact  in  both  the  vertical  and 
the  horizontal  planes,  we  may  write     e^  =  e^  tan  go. 

The  following  system  is  evidently  applicable  to  computing 
the  results  of  firing  against  either  horizontal  or  vertical 
planes. 

EXAMPLE. 

Suppose  we  fire  10  shots  over  water  with  the  sight  fixed 
at  the  estimated  distance  of  the  target,  or  1000  yards.  The 
first  shot  falls  50  yards  beyond  and  10  yards  to  the  left,  and 
so  on  as  shown  in  the  following  table.  Shots  falling  beyond 
the  origin  and  those  going  to  the  right  of  it  are  estimated 
positively.    Suppose  that  we  obtain  the  following  record. 


26 


XXX. — ACCURACY    OF    FIRE. 


COMPUTATION. 


DEVIATIONS. 

EKRORS. 

SQUARES  OP 

ERRORS. 

No. 

r,  etc.  = 

of 
Fire 

In  Range. 

Lateral. 

In  Range. 

Lateral. 

In  Range. 

Lateral. 

(^+<)' 

+ 

- 

+ 

- 

+ 

- 

+ 

'! 

1 

1. 

50 

10 

25 

8 

625 

64 

26 

2. 

30 

5 

55 

7 

3025 

49 

55 

3. 

20 

15 

5 

17 

25 

289 

18 

4. 

100 

6 

75 

4 

5G25 

16 

■(5 

5. 

70 

4 

95 

2 

90i5 

4 

95 

6. 

150 

20 

125 

18 

15625 

324 

126 

7. 

60 





85 

2 

7225 

4 

85 

8. 



10 

25 

12 

625 

144 

2S 

9. 

90 

10 

65 

8 

4225 

64 

66 

10. 

— 

— 

25 

2 

625 

4 

25 

Total       410 
—160 

160 

30 

50 
-30 

290 

+290 

290 

40 

+40 

40 

^V  1=46650 

^17, =962 

10)600 
£  —00  0 

10)250 

10)20 

10)580 

10)80 

+  25.0 

—2.0 

£,=58.0 

£2=8.0 

Mean  deviation  in  range = 

Mean    error 

in    range 

+  25.0  yds. 

=  58.0  yd 

3. 

Mean  lateral  deviation  = 

Mean     latera 

1    error  = 

-2.0  yds. 

=8.0  yds. 

From  the  above  computation  and  figure  20  it  appears 
that  the  mean  range  is  1025  yards,  so  that  if  the  elevation 
had  been  taken  for  975  yards  the  target  would  have  been 
more  probably  hit. 

The  shaded  rectangle  of  figure  20  represents  the  plan  of 
a  vessel:  it  applies  to  the  subject  of  Probability  of  Fire  yet 
to  be  discussed. 


Note. — When  the  mean  range  is  correctly  found  the  +  errors  are 
equal  to  the  —  errors  of  the  same  kind.  This  tests  the  accuracy  of  the 
work.  It  is  not  necessary  however  that  fractional  parts  of  yards  should 
enter  into  the  value  of  the  mean  range. 


XXX. — ACCURACY    OF    FIRE.  27 

Swiss  Method. 

When  the  number  of  shot  marks  is  very  great,  as  in 
volley  firing  with  small  arms,  it  may  be  very  difficult  to 
measure  all  the  individual  shot  marks  without  error.  The 
following  method  may  then  be  employed.     See  figure  20'. 

Count  the  total  number  of  shot  marks  =  n.  Then  hold- 
ing a  straight  edge  horizontally  slide  it  over  the  face  of  the 

fi 
target  until  -  marks  lie  above  it;  indicate  this  by  a  hori- 
zontal line.  Draw  similar  lines  for-— and  — -,  and  repeat  the 

process  with  the  straight  edge  vertical. 

We  may  thus  approximate  closely  to  the  measurement  of 
all  the  elements  of  the  computation;  but  we  must  assume 
that  all  the  shots  strike  the  target. 

III.   PROBABILITY. 

By  the  probability  of  hitting  a  target  under  certain  circum- 
stances is  meant  the  ratio  of  the  number  of  times  that  the 
target  would  be  hit  to  the  whole  number  of  shots  fired,  sup- 
posing the  number  of  shots  fired  under  these  circumstances 
to  be  infinite. 

Here  unity  is  the  mathematical  symbol  for  certainty,  so 
that  a  probability  of  \  or  25  per  cent,  signifies  that  one  hit 
may  reasonably  be  expected  from  four  independent  shots 
fired  under  the  same  circumstances. 

If  the  same  ratio  held  with  a  finite  number  of  shots  we 
could  calculate  with  certainty  beforehand  the  number  of  shots 
necessary  to  yield  a  certain  number  of  hits.  But  in  practice 
the  ratio  is  not  certain,  but  only  approximate  ;  the  approxi- 
mation increasing  with  the  number  of  shots  upon  which  the 
calculations  are  based. 


28  XXX. — ACCURACY   OF   FIRE. 

Probability  Curve. 

Suppose  we  take  as  an  origin  a  point  at  a  distance  from 
the  gun  equal  to  the  mean  range,  and  lay  off  the  errors  to 
the  right  and  left  of  this  point  according  as  they  are  pos- 
itive or  negative.  If  then,  corresponding  to  each  error  in 
range  as  an  abscissa  we  draw  an  ordinate  of  a  length  pro- 
portionate to  the  probability  of  that  error,  the  coordinates 
so  obtained  will  be  those  of  the  points  of  a  curve  known  as 
Probability  Curve,  figure  21. 

The  general  form  of  this  curve  will  appear  from  consid- 
ering; 

1.  That  small  errors  are  more  probable  than  large  ones, 
and  therefore  that  the  ordinates  will  be  greatest  for  the 
smallest  errors.* 

2.  That  postive  and  negative  errors  are  equally  probable, 
and  therefore  that  the  probability  curve  will  be  symmetrical 
about  the  axis  of  S. 

3.  That  large  errors  are  not  practically  to  be  expected; 
since  such  errors  would  come  under  the  head  of  avoidable 
mistakes. 

4.  That  the  curve  will  have  the  axis  of  X  as  an  asymp- 
tote; since,  theoretically,  the  only  error  that  can  never  be 
committed  is  one  that  is  infinitely  great. 

The  equation  of  the  probability  curve  is 

in  which  s  is  the  probability  of  an  error  of  the  magnitude 
x;  e  is  the  base  of  the  Napierian  system  of  logarithms,  a:id 
h  is  the  measure  of  precision,  the  value  of  which  is  found 
to  be 

^  =  \/^>  (3) 

*  See  remark  as  to  the  density  of  the  sheaf  of  trajectories,  page  6. 


XXX.— ACCURACY   OE   FIRE.  29 

in  which  n  is  the  number  of  shots  fired,  and  ^z;^  is  the 
sum  of  the  squares  of  the  errors  in  the  direction  in  which 
these  are  estimated. 

By  multiplying  both  members  of  Eq.  (1)  by  dx  and  inte- 
grating between  limits  x^  =  OM  and  x^^ON  we  may 
obtain  the  probability  of  committing  an  error  in  range 
between  the  two  errors  x^  and  ^„,  or 

h  /•  /jv-2   2 

P=—^f^-e  dx=  2iVQ2i  RMNL.  (3) 

The  total  area  between  the  curve  and  the  axis  of  X  is 
unity,  so  that,  for  a  particular  curve  in  which  range  errors 
only  are  considered,  if  the  area  R  M N L  =  ^,  the  mean- 
ing of  the  case  would  be,  that  when  the  center  of  the 
group  of  shot  marks  was  at  O,  a  target,  the  length  of 
which  measured  in  the  plane  of  fire  is  MN,  and  the  width 
of  which  at  right  angles  to  the  plane  of  fire  is  infinite,  and 
which  is  situated  at  the  distance  O M  from  the  center  of 
the  group  could  reasonably  be  expected  to  be  struck  by 
one  tenth  the  number  of  shots  fired  at  it;  the  certainty  of 
prevision  increasing  with  the  accuracy  with  which  h  is 
known,  or  with  n,  Eq.  (2). 

It  is  evident  that  the  above  discussion  applies  as  well  to 
lateral  errors  as  to  errors  in  range,  and  that  for  each  gun 
and  range  an  infinite  number  of  probability  curves  exists, 
depending  upon  the  directions  assumed  fo^  the  axes.  Of 
these  we  shall  consider  but  two,  but  it  is  well  to  remember 
that  the  others  together  form  the  surface  of  probability j\ 

Note. — For  the  deduction  of  these  equations  and  for  the  fuller  treat- 
ment of  the  subjects  herein  discussed  see  the  work  on  "  The  Accuracy 
and  Probability  of  Fire  "  by  Ensign  J.  H.  Glennon,  U.  S.  N.  The  sub- 
ject is  treated  in  other  works  on  Probability,  and  Least  Squares. 

f  Consider  an  infinite  number  of  shots  fired  against  a  target.  Im- 
agine that  after  firing  all  the  projectiles  are  arranged  upon  the  points  on 


30  XXX. — ACCURACY   OP   FIRE. 

figure  22,  the  volume  between  which  and  that  portion  of  the 
plane  of  reference  bounded  by  any  plane  figure  is  propor- 
tional to  the  probability  of  striking  an  object  of  the 
dimensions  and  position  of  the  figure  at  the  range  and 
under  the  circumstances  in  question. 

Since,  from  the  symmetry  of  the  probability  curve  the 
integral  between  the  limits  —  x  and  +  x  Eq.  (3)  is  twice 
the  integral  from  — ^  to  O,  or  from  O  to  -\-x,  we  have 

as  the  probability  that  a  it  error  in  range  taken  without 
regard  to  its  sign  is  numerically  less  than  x. 

Taking  /ix  as  one  variable,  the  values  of  I*  correspond- 
ing to  its  different  numerical  values  have  been  calculated 
and  are  arranged  in  the  following  Table  I. 

Example. — Suppose  it  be  desired  to  compute  the  chance  of 
hitting  the  deck  of  a  ship  300  feet  long  and  36  feet  wide 
(100  yds  by  12  yds.),  the  keel  of  the  ship  being  in  the  plane 
of  fire  and  the  center  of  the  ship  being  at  the  mean  point 
of  impact.  The  circumstances  being  those  given  in  the 
preceding  example. 


We  have  h^  =  \/  -^r^^r-^  "  \/  93300  ^  ~M  "^  ().^(^^^. 

Therefore,  supposing  for  the  present  that  the  ship  is  of 
indefinite  width  or  that  we  are  firing  at  a  belt  or  zone  at 
right  angles  to  the  plane  of  fire  and  limited  by  parallel 
lines  at  50  yards  on  each  side  of  the  mean  point  of  impact; 


which  they  struck,  being  superposed  one  upon  the  other  upon  the  ele- 
mentary surfaces  upon  which  they  fell.  The  mass  of  projectiles  will  thus 
form  a  volume  bounded  by  the  surface  of  probability  and  the  target. 


XXX. — ACCURACY    OF    FIRE. 


31 


P^ 


TABLE  I. 

PROBABILITY    OF    ERRORS, 
2         ^.^       —h^x^ 


S'Tt  J  0 


d  {hx), 


hx 

P 

hx 

P 

hx 

P  ' 

hx 

1 

P 

hx 

P 

0.00 

0.00000 

0.40 

0.42839 

0.80 

0.74210 

1.20 

0.91031 

1.60 

0.97635 

.02 

.02256 

.42 

.44747 

.82 

.75381 

1.22 

.91553 

1.62 

.97804 

.04 

.04511 

.44 

.46622 

.84 

.76514 

1.24 

.92050 

1.64 

.97962 

.06 

.06762 

.46 

.48465 

.86 

.77610 

1.26 

.92523 

1.66 

.98110 

.08 

.09008 

.48 

.50275 

.88 

.78669 

1.28 

.92973 

1.68 

.98249 

.10 

.11246 

.50 

.52050 

.90 

.79691 

1.30 

.93401 

1.70 

.98379 

.12 

.13476 

.52 

.53790 

.92 

.80677 

1.32 

.93806 

1.72 

.98500 

.14 

.15695 

.54 

.55494 

.94 

.81627 

1.34 

.94191 

1.74 

.98613 

.16 

.17901 

.56 

.57161 

.96 

.82542 

1.36 

.94556 

1.76 

.98719 

.18 

.20093 

.58 

.58792 

.98 

.83423 

1.38 

.94902 

1.78 

.98817 

.20 

.22270 

.60 

.60386 

1.00 

.84270 

1.40 

.95228 

1.80 

.98909 

.22 

.24429 

.62 

.61941 

1.02 

.85084 

1.42 

.95537 

1.82 

.98994 

.24 

.26570 

.64 

.63458 

1.04 

.85865 

1.44 

.95830 

1.84 

.99073 

.26 

.28690 

.66 

.64938 

1.06 

.86614 

1.46 

.96105 

1.86 

.99147 

.28 

.30788 

.68 

.66378 

1.08 

.87333 

1.48 

.96365 

1.88 

.99216 

.30 

.32863 

.70 

.67780 

1.10 

.88020 

1.50 

.96610 

1.90 

.99279 

.32 

.34912 

.72 

.69143 

1.12 

.88679 

1.52 

.96841 

1.93 

.99338 

.34 

.36936 

.74 

.70468 

1.14 

.89308 

1.54 

.97058 

1.94 

.99392 

.36 

.38933 

.76 

.71754 

1.16 

.89910 

1.56 

.97263 

1.96 

.99443 

.88 

.40901 

.78 

.73001 

1.18 

.90484 

1.58 

.97455 

1.98 
2.0 
3.0 

00 

.99489 

.99532 

.99998 

1.00000 

32  XXX. — ACCURACY   OF   FIRE. 

the   permissible   error   is  ±  50  yds  =::v  .*.  >^^  =  0.  49  and 
/i*  from  the  table  is  about  0.51. 

Similarly  for  the  lateral  precision; — 

^2  =  i /     ^      =  0.0684  and  h^x-=  0.41, 
y    1924 

and  p^  from  the  Table  is  about  0.43. 

That  is,  that  about  43  per  cent  of  the  shots  will  fall  with- 
in a  belt  6  yds.  wide  on  each  side  of  the  plane  of  fire. 

Now,  from  the  theory  of  probabilities,  the  probability  of 
the  concurrence  of  two  events  is  the  product  of  the  proba- 
bility of  each  of  the  two  events  when  considered  separately; 
the  probability  that  a  shot  will  fall  within  both  belts  is 
/o  =  0.51  X  0.43  =  0.22 

OTHER  MEASURES  OF  INACCURACY. 

Probable  Error. 

In  case  that  hx  is  so  chosen  that  P  in  Eq.  (4)  is  equal 
to  J,  the  probability  of  committing  an  error  numerically  less 
than  X  is  equal  to  that  of  committing  an  error  numerically 
greater  than  x.  Such  a  value  of  x  is  called  the  probable 
error,  or  r.  By  interpolating  in  Table  I  it  is  found  that 
for  P  =  \,hx  =  hr  —  0.4769,  or 


r  =  -^iZ^  =  0.4769  yi /  ^^^^^^  =  0.6745 


/4^i 


The  term  probable  error  is  a  misnomer.  Its  true  mean- 
ing may  be  illustrated  by  reference  to  figure  21  in  which  if 
x  =  r=OM  be  so  taken  that  O SMR  =  J  then,  from  the 
symmetry  of  the  curve  2  0SMP  =  ^;  or  2r  will  be  the 
width  of  the  space,  measured  equally  in  both  directions 
from  the  mean  point  of  impact,  within  which  the  shots  are 

*  The  symbols  /i  /g  /a  correspond  to  the  nomenclature  page  24. 


XXX. — ACCURACY    OF    FIRE.  33 

as  likely  to  fall  as  not,  or  within  which  there  is  an  even 
chance  of  striking.  The  accuracy  varies  inversely  with  the 
magnitude  of  this  error. 

True  Mean  Error. 

The  probable  error  must  not  be  confused  with  the 
mean  error  already  found.  In  the  example  the  probable 
error  in  range  is  r  =  48.5  yds.  and  the  mean  error  is  58 
yds.  The  latter  value  is  only  an  approximation  to  the 
true  mean  error^  for  which  the  symbol  is  x.  From  the 
equation  of  the  probability  curve  this  has  been  found 

-__      1 

or  in  the  example,  ^  =  57  yards:  very  nearly  the  mean 
error. 

By  combining  the  expressions  for  x  and  r  we  find  the 
ratio 

-^  =  0.8453.  (6) 

X 

Probable  Zones  and  Rectangles. 

From  the  foregoing  example  we  see  that  the  true  mean 
error  does  not  differ  materially  from  the  computed  mean 
error  obtained  with  a  fair  number  of  shots. 

Also,  that  since  the  positive  and  negative  errors  are  equal, 
if  r  be  the  probable  error  in  either  direction  from  the  mean 
point  of  impact,  2r  =  1.69  x  will  be  the  width  of  a  zone 
measured  at  right  angles  to  the  direction  of  the  error  that 
will  contain  half  the  number  of  shot  marks. 

This  measure  is  much  used  in  the  British  service  in 
which  the  mean  error  in  range   X   1.69  gives  very  nearly 


*  In  the  mathematical  course  this  is  called  the  mean  error. 


34  XXX. ACCURACY    OF    FIRE. 

the  width  (in  the  plane  of  fire)  of  the  length  zone,  figure  23. 
See  page  38. 

Similarly,  the  mean  lateral  error  x  1.69  gives  the  width 
(at  right  angles  to  the  plane  of  fire)  of  the  breadth  zone^ 
figure  24. 

The  mean  vertical  error  x  1.69  —  the  mean  error  in 
range  xtano?  x  1.69,  gives  the  width  (vertically)  of  the 
height  zone. 

Referring  to  the  horizontal  plane,  the  intersection  of  the 
length  and  breadth  zones  gives  a  rectangle  probably  con- 
taining \  of  ^,  or  \  of  the  whole  number  of  shots.  See 
pages  27  and  32.     This  is  called  the  ^h  per  cent  rectangle. 

The  Probable  Rectangle  is  the  50  per  cent  rectangle,  or 
is  the  rectangle  of  which  (the  center  being  at  the  mean 
point  of  impact,  and  the  sides  being  parallel  to  the  directions 
in  which  the  errors  are  measured)  the  sides  are  respectively 
proportional  to  the  probable  errors  in  the  same  directions, 
and  the  probability  of  hitting  within  it  in  either  direction  is 


=  ^"1=0.7071.1 


By  reference  to  Table  I,  we  find  that  for  /'^z:  0.7071, 
hx  =  0.7438. 

By  substituting  the  value  of  h  (Eq.  2)  we  have  for  the  sides 
of  the  probable  rectangle  — 

length  =  2  X,  =  2.104  \J ^  (6) 

breadth  =  2  ^,  :=  2.104  y  ~i  (7) 

Remark. 

The  probable  rectangle  is  seen  to  be  useful  in  comparing 
the  accuracy  of  two  guns  by  comparing  the  magnitudes  of 
the  errors  which  they  will  make  with  equal  facility. 


XXX. ACCURACY    OF    FIRE.  35 

Its  determination  is  based  on  the  Theory  of  Probabilities, 
but  is  only  indirectly  connected  with  the  probability  of 
hitting  at  a  single  shot  a  target  the  dimensions  and  position 
of  which  are  known. 

Accuracy  of  a  Gun. 

The  probable  rectangle  in  the  horizontal  plane  will  vary 
in  dimensions  for  different  guns  and  different  mean  ranges, 
and  its  size  will  be  an  inverse  measure  of  the  accuracy  of 
the  gun  for  the  mean  range  for  which  it  is  calculate<i. 

Unless  the  angle  of  fall  is  the  same  for  the  different 
guns  in  question,  the  relative  accuracy  as  determined  by 
the  size  of  the  i)robable  rectangle  in  the  vertical  plane  will 
be  very  different  from  that  determined  in  the  horizontal 
plane.  A  gun  having  a  very  flat  trajectory  is  placed  at  a 
disadvantage  when  its  accuracy  is  measured  by  the  size  of 
its  probable  rectangle  in  the  horizontal  plane;  and,  in  gen- 
eral, the  more  nearly  the  plane  of  the  target  coincides  with 
direction  of  the  fall  of  the  projectiles,  the  greater  is  this 
disadvantage.  On  the  other  hand,  guns  are  placed  on  the 
sam«=»  footing,  and  each  shows  best  its  accuracy  when  the 
target  plane  for  each  gun  is  chosen  perpendicular  to 
the  trajectory  at  the  mean  point  of  impact.  Against 
vulnerable  horizontal  targets,  as  the  decks  of  ships,  better 
results  may  therefore  be  expected  with  rifled  mortars  than 
with  high  powered  guns;  unless  these  latter  are  mounted 
in  a  commanding  position,  or  the  muzzle  velocity  is  so  re- 
duced, as  to  give  a  large  angle  of  fall  on  the  horizontal 
plane  in  question. 

Probability  of  Hitting  an  Object  of  any  Form. 

Table  I  may  be  used  for  finding  the  probability  of  hitting 
a  target.  As,  however,  the  probable  errors,  laterally  and 
in  range,  would  usually  be  given,  a  more  convenient  table 


S6 


XXX. — ACCURACY    OF    FIRE. 


X. 


IS  one  in  which  the  argument  is  -*  This  is  readily  formed 
from  Table  I  by  remembering  the  relation  between  /i  and 
r,  or  -  =  ____-  whence, 


0.4769 


^x 


r  ~~  0.4769  ^^ 

Table  II,  known  as  Chauvenet's  table,  is  to  be  used  after 
the  manner  of  a  table  of  logarithms.     Thus  for  a  value  of 

X 

-=0.40    the   corresponding   probability   is   0.21:     Con- 
versely, a  probability  of  0.535,  or  53^  per  cent,  corresponds 

X 

to  a  value  of  —  =  1.08. 
r 

In  figure  25  is  plotted  the  curve  expressing  the  relation 


between  —  and  F, 
r 


F  = 


TABLE  II. 

PROBABILITY    OF    ERRORS, 

2       .*    —t^ 


dt,    t 


X 


>^jt:  =  0.4769 - 
r 


P. 

0 

1 

2 

3 

4 

6 

6 

7 

8 

9 

0.0 

0 

.02 

.04 

.06 

.07 

.09 

.11 

.13 

.15 

.17 

.1 

.18 

.20 

.22 

.24 

.26 

.28 

.30 

.32 

.34 

.36 

.2 

.38 

.40 

.41 

.43 

.45 

.47 

.49 

.51 

.53 

.55 

.3 

.57 

.59 

.61 

.63 

.65 

.67 

.70 

.72 

.74 

.76 

.4 

.78 

.80 

.82 

.84 

.86 

.89 

.91 

.93 

.95 

.98 

.5 

1.00 

1.02 

1.04 

1.07 

1.09 

1.12 

1.14 

1.17 

1.19 

1.22 

.6 

1.25 

1.27 

1.30 

1.33 

1.36 

1.39 

1.42 

1.45 

1.48 

1.51 

.7 

1.54 

1.57 

1.60 

1.64 

1.67 

1.71 

1.74 

1.78 

1.82 

1.86 

.8 

1.90 

1.94 

1.98 

2.03 

2.08 

2.13 

2.18 

2.24 

2.30 

2.37 

.9 

2.44 

2.52 

2.60 

2.69 

2.78 

2.91 

3.04 

3.22 

3.45 

3.82 

XXX. — ACCURACY   OF    FIRE. 


RECTANGULAR   OBJECT. 

In  figure  26  suppose  O  is  the  mean  point  of  impact  of  a 
number  of  shots  in  the  horizontal  plane,  OX  the  direction 
in  which  range  errors  are  measured,  and  (9  F  perpendicular 
to  OX,  the  direction  in  which  lateral  errors  are  measured. 
Required  the  probability  of  hitting  the  rectangle  A  B  CD, 
of  which  O  is  the  center,  A  B  and  B  C  being  parallel  to 
OX  and  O  Y, 

Let  ri  and  r^  be  the  probable  errors  of  the  gun  in  range 
and  laterally  under  the  circumstances. 

The  probability  of  committing  an  error  in  range  less 
numerically  than  OE  is,  found  in  the  table  for 
x__  O  E 

The  probability  of  committing  a  lateral  error  less  num- 
erically  than    OF  IS  found   likewise  in  the   same    table 

OF 

for    ■.     The  probability  of  the  concurrence  of  these 

two  events  is  the  probability  of  hitting  inside  the  rectangle 
A  BCD,  which  is  therefore  the  product  of  the  two  prob- 
abilities found. 

The  probability  of  hitting  inside  the  rectangle  O  F B  E 
is  \  the  probability  of  hitting  inside  the  rectangle  A  BCD; 
since  numerically  equal  positive  and  negative  errors  are 
equally  probable,  and  the  probability  of  hitting  A  BCD  is 
the  sum  of  the  probabilities  of  hitting  the  four  smaller 
rectangles  into  which  it  is  divided. 

The  probability  of  hitting  inside  the  rectangles  OFM N 
and  O LRE  is  found  in  the  same  way  as  that  of  hitting 
inside  OFBE. 

The  probability  of  hitting  inside  NM B E  is  that  of 
hitting  inside  OFBE  minus  that  of  hitting  inside  OFMN, 
Similarly  for  LFBR,  LFMK  and  NKRE. 


38  XXX. — ACCURACY    OF    FIRE. 

The  probability  of  hitting  KMB  R  is  that  of  hitting 
NMBE  minus  that  of  hitting  N K R E. 

ANY    PLANE    FIGURE. 

Any  plane  figure  may  be  divided  (approximately)  into 
small  rectangles  and  the  probability  of  hitting  each  rec- 
tangle found.  The  sum  of  the  separate  probabilities  may 
then  be  found,  and  this  will  be  the  probability  of  hitting 
the  figure. 

In  what  has  preceded  we  have  used  horizontal  targets. 
There  is  nothing  in  the  method,  however,  that  will  not 
apply  equally  well  to  vertical  targets  if  we  substitute  ver- 
tical for  range  errors. 

EXAMPLES   IN    THE    PROBABILITY    OF    FIRE. 

Although  the  value  of  the  probable  error  may  be  ascer- 
tained, the  computation  may  be  abbreviated  by  assuming 
that  the  true  mean  error,  x^  does  not  differ  materially  from 
the    mean    error    f,  determined    as   shown    on    page    24. 

So  that  in  Table  II  the  ratio  —  may  be  taken  as  equal  to 
2^  2j\?  2x 


2^        2  x0.845  a:        1.69  e* 

from  which  the  corresponding  probability  may  be  found. 

The  same  results  are  obtained  by  the  English  method  of 
using  the  50  per  cent  zones,  as  follows: 

This  considers  that  the  width  of  the  50  per  cent  zone  is 
unity,  see  Table  II,  and  therefore,  (the  probable  error  of  the 
gun  being  constant  for  the  same  range  and  circumstances) 
that  the  width  of  other  zones  containing  a  per  cent  of  shots 
greater  or  less  than  50  per  cent  is  proportional  to  the  cor- 


XXX. — ACCURACY    OF    FIRE.  39 


2x 
responding   value    of    — ;  2r  representing    the   width    of 
2r 

the    50  per   cent   zone.      And   conversely,  that   when   the 

ratio  -  is  known,  the  probability  of  striking  within  the  given 
r 

zone  is  that  given  by  the  corresponding  value  of /'in  Table  II. 

Data. 

For  a  given  gun  under  given  conditions  we  have— 
E  =  4945  yds.;  cj  =  7°  25':  e,  =19.4  yds.;  e,=  1.8  yds.; 
^3  =  19.4  X  tan  7°  25'  =  2.5  yds. 

Suppose  that  unless  otherwise  stated  the  mean  point  of 
impact  is  at  the  center  of  the  target. 

1.  Determine  the  probability  of  striking  a  raft  12  yds. 
square  at  the  range  R, 

9y-  19 

ri!= — =  4  .  •.  A.  =  1,  or  practical  cer- 

2/2       1.8  X  1.69 

tainty ;  and    about    1    out  of  5    shots  may  be    expected  to 
strike  the  raft. 

2.  Suppose  the  target  to  be  of  the  same  dimensions  and 
vertical :  we  have  /^  =  1 ;  /3  =  0.945  =/o-     See  page  85. 

3.  If  a  zone  of  a  certain  width  catches  20  per  cent  of  the 
shots  fired,  how  much  wider  must  another  zone  be  to  catch 
80  per  cent? 

From  Table  II  we  have  for  /  =  20  per  cent,  —  =  0.38 

x' 
and  for /  =  80  per  cent, —  =1.90,  and  smce  r  is  constant 

—  :  -  ::  1.90  :  0.38    or    ^'  =  5  x. 
r       r 


40  XXX. — ACCURACY    OF    FIRE. 

4.  Suppose  that  the  mean  point  of  impact  is  at  the  middle 
of  the  lower  edge  of  a  target  8  feet  square.  (The  case  cor- 
responds to  firing  at  the  water  line  of  a  vessel.) 

We  suppose  the  target  to  be  extended  downward  by  an 
amount  equal  to  its  height,  and  take  for  p^  half  the  prob- 
ability of  striking  the  whole  target:  we  have 

/2  =  0.45;  A  =  -^    •••    A  =  0.135. 

5.  What  would  be  the  effect  of  raising  the  mean  point  of 
impact  2  feet  on  the  above  target? 

Suppose  that  target  to  be  extended  downward  4  feet,  as 
in  figure  27.  Then  the  target  may  be  supposed  to  be  com- 
posed of  two  portions  a  and  b,  the  former  of  which  is  half 
the  height  of  a  target  12  feet  high,  and  the  other  portion 
half  the  height  of  a  target  4  feet  high. 

We  find  for  a     p^  =  ^^  =  0.24 

2 

and  for  ^  p/  =  ^  =  0.085 


.-.    /3=  0.325 

and    /o==  0.146. 

6.  Suppose,  as  in  figure  28,  that  there  are  two  targets  8 
feet  square  and  8  feet  apart  fired  at  from  the  above  gun  and 
at  the  above  range.     Which  plan  would  give  the  greater 
number  of  hits  in  the  two  targets  collectively : 
1st.  To  aim  at  the  center  (a)  of  one  ? 
2nd.  To  aim  at  the  center  ^^)  of  the  space  between 
the  two  ? 
We  will  suppose  the  mean  point  of  impact  will  fall  on  the 
point  aimed  at,  and,  as  the  mean  vertical  error  will  be  con- 
stant, we  may  neglect  it  in  making  the  comparison  desired. 


XXX. — ACCURACY    OF    FIRE.  41 


First  Case. 

For  the  target  aimed  at  we  have  //  =  0.45. 

Now,  consider  the  target  (4  +  8  +  8)  x  2  =  40  feet  wide, 
and  take  one  half  the  resulting  value  of  p^  or  p^'  =  0.50. 

Similarly  consider  the  target  (4  +  8)  x  2  =  24  feet  wide 
and  find  //"  =  0.47. 

Then, /a"  — //"  =  0.03  is  the  probability  of  hitting  the 
target  not  aimed  at,  and  p^  =//  +  (//'  — //"  )  =  0.48  will 
be  the  probability  for  both  targets. 

Second  Case. 

Considering  the  target  24  feet  wide    p^   =  0.947 
and  for  the  middle  space  A"==  ^-^^ 


A  =  0.497. 


RIGHT    LINE   METHOD. 

The  abscissa  of  the  center  of  gravity  of  the  area  included 
between  the  axes  OX  and  OS  and  the  probability  curve 
A  B  Cf  figure  29,  is  evidently  the  frue  mean  error,  x,  or  the 
arithmetical  mean  of  an  infinite  number  of  errors. 

If  we  draw  D  E  so  that  the  centers  of  gravity  oi  D  O  E 
and  O  A  B  C  a:^   O  shall  coincide,  and  call  O  E  —  m,  then 

D  O  E  =  O  A  B  'C  ^  O  =  h  2cci^  D  O  =  -' 

m 

From  the  properties   of  the   triangle   the   abscissa  of  the 

171 

center  of  gravity  oiDOE^  —  =E\  and  if  the  probability 

o 

curve  were  considered  to  be  a  right  line  we  would  have  x  =  e. 
Given  then  the  mean  error,  e,  the  line  D  E  would  be  deter- 
mined. 

In  case  the  right  line    method  were  strictly  accurate, 


42  XXX. — ACCURACY    OF    FIRE. 

there  would  be  no  possibility  of  committing  an  error  greater 
them  m^  which  would  therefore  be  an  extreme  error. 

Let  us  see  from  the  probability  curve  what  would  be  the 
probabiHty  of  committing  an  error  less  than  in.  We  have, 
assuming  e  =  x.     See  page  33. 

3 


h 


^Jn' 


m  =  3x  mean  error  = 

3 

whence  /im= — ; —  =  1.6925. 

Referring  to  Table  I,  we  find  the  corresponding  proba- 
bility 0.983;  that  is,  98  per  cent  of  the  shots  will  make  an 
error  less  than  three  times  the  mean  error:  a  close  approxi- 
mation. 

Also  making   x=  0,   in  Equation  (1.) 

we  have  the  value  of  the  maximum  ordinate  of  the  proba- 
bility curve.     It  is 

L=^V^  =  ___J___ 

•^0  ~   ^^  ^r~        7t  X  mean  error ' 

Similarly  the  corresponding  ordinate  in  the  case  of  the 
right  line  is 


3  X  mean  error* 
or  slightly  greater  than  the  probability  curve. 

These  differences  are  not  material.  The  approximation  in 
other  cases  is  shown  by  figure  29;  the  probability  of  com- 
mitting an  error  between  O  and  -{-  x  {=  O  J*')  being,  ac- 
cording to  the  probability  curve,  the  area  O  A  B  F^  and 
according  to  the  right  line  the  area  ODGF.  Experience 
also  shows  that,  in  firing  projectiles,  the  extreme  error  is 
a  little  more  than  three  times  the  mean  error,  but  this  is  not 
of  great  importance;  all  that  is  necessary  is  that  the  proba- 


XXX. — ACCURACY    OF    FIRE.  43 

bility  of  exceeding  this  error  should  be  small   enough  to 
be  neglected,  and  we  cannot  have  any  doubt  in  this  respect. 

Equation  of  the  Eight  Line. 

In  the  two  triangles    ODE  and   FGE,   tan   DEO=^ 

CE  DO 

-j^-pr^  =  -TTTF-or  Substituting for  G E,  EE,  DO  2ind  OE 
EE  OE  ^  '         ' 

their  values,  s,  m  —  x^    —  and  m,  respectively,  we  have 


(9) 


m  —  X 


m 

1 

m  —  X 

m"' 

°'  ^-     m'    ' 

as  the  equation  of  the  line  D  E. 

The  probability  of  hitting  within  a  small  length  dx,  at  x 
is  then 

pz=zs  dx  — ^  dx.  (10) 

Probability  of  Hitting  any  Plane  Figure. 

Suppose  positive  errors  in  range  are  measured  in  the 
direction  OX  figure  32,  from  the  mean  point  of  impact  O^ 
O  M  being  equal  to  m^  the  extreme  error  in  range. 

Following  out  the  supposition  of  the  two  causes  of  error, 

suppose  positive  lateral  errors  are  measured  in  the  direction 

of  the  axis  O  Y,  (9  iV  being  equal  to  «,  the  extreme  lateral 

error. 

w  ~~  X 
li  D  C  represent  dx,  p^  = g—  dx,    is  the  probability 

of  hitting  somewhere  between  the  lines  AD  and  B C,  dis- 
tant -\-  x\w  range  from  the  mean  point  of  impact. 

n  — y 
If  KR  represent  dy,  p^  =  — g—  dy,    is  the   probability 

of  hitting  between  the  lines  ET  and  -^^S",  distant  +  y  lat- 
erally from  the  mean  point  of  impact. 


44  XXX. — ACCURACY    OF    FIRE. 

The  small  area  A'  B'  C  D'  fulfills  both  these  conditions 
and  the  probability  of  hitting  it  is  therefore 

m—x.      n—y     , 
pxy  = «-  dx    — /-  dy. 

If  we  denote  by  Z>"  D  and  A"  D,  figure  32,  by  y^  and  y^ 
respectively,  the  probability  of  hitting  between  two  lines 
drawn  through  the  points  £>"  and  A'^  parallel  to  O  X  is 


PJ=/:^^y. 


If  however,  we  limit  the  target  in  the  direction  of  the 
range  errors  to  the  length  dx  at  +  x,  the  probability  of 
hitting  the  target,  which  is  represented  by  A''  B"  C"  D"  is 

If  y^-=f^{x)  and  jJ^2=/2  (^)  are  the  equations  of  two 
curves  H D"  G  and  E  A'*  F  we  can  write 

=  ^Z^^. /•/«(-)   ^li:^dy^F(x)dx, 

as  the  probability  of  hitting  any  elementary  area 
A''  B''  C  B>'\ 
Calling  O  Z.  a^,  and  O  K^  a^^  the  probability  of  hitting 
the  figure  E  F  G  If  is 


XXX. —  ACCURACY    OF    FIRE.  45 

Remark. 

Caution  is  necessary  in  using  the  right  Hne  method.  The 
ordinates  of  the  prolonged  hne  D  E^  figure  29,  to  the  right 
of  E  do  not  represent  probabihties,  nor  do  they  to  the  left 
of  D.  As  a  consequence,  in  the  figure,  first  ^i,  a^^  yi^y^ 
must  be  positive  ;  second,  when  either  of  these  exceeds  the 
extreme  error  in  its  direction,  it  must  be  placed  equal  to 
that  extreme  error.  The  probability  of  hitting  a  figure,  part 
of  which  is  in  each  of  the  quarters  of  the  extreme  rectangle 
surrounding  the  mean  point  of  impact,  is  obtained  by  ad- 
ding together  the  probability  of  hitting  the  parts,  calculated 
separately.  Distances  measured  along  the  axes  OX  and 
O  Y  from  the  mean  point  of  impact  are  regarded  as  pos- 
itive in  each  quarter. 

It  will  be  noted  that  this  method  dispenses  with  the  use 
of  the  tables. 
Abbreviation  of  the  Right  Line  Method. 

In  figure  30  the  probability  of  an  error  less  than  x  will 
be  the  quotient  of  the  area  of  the  trapezoid  above  x  by  the 
area  of  the  triangle  above  m.  Call  these  areas  T  and  A 
and  let  e  be  the  abscissa  of  the  center  of  gravity  of  the 
triangle,  then  3  e  =  m. 

We  have 


-•v'>- 

From  the  similarity  of  the  triangles 

m 

■6e 

-(-0 

30                                     sm      3  s  s 

or 


46  XXX. — ACCURACY    OF    FIRE. 


Therefore 


Jy     _        T     _%  X  1       [X\^ 


This  gives  a  formula  that  can  be  very  easily  memorized. 
See  below. 
Application  to  Different  Figures. 

Rectangle. — In  figure  31,  denotin-g  O  F  hj  a,  and  O  E 
by  b,  the  probability  of  hitting  the  rectangle  E  A  F  O  is 

^mn\         m  J     \         nj 

The  probability  of  hitting  the  rectangle  D  A  B  C  of 
which  the  center  is  at  the  mean  point  of  impact,  is  four 
times  the  probability  for  E  A  F  0;  or 

°        m  n    \         in  J     \        nj 


'%a 
m 
or,  since   m  =  Z  e^  and  n  =  ^  e^, 


^»-  [si  -  9  0  J   ""   [37,      9"  (1;)  J  • 

Applying   this   method   to  example   page   30,  we  have, 
since  w  =  58  x  3  =  174  and  ;?  =  8  x  3  =  24 

rioo     /  50  \n     ri2     /6  \n 
^-[m-(m;J"L24-(24)J 

=  0.4922  X  0.4375  =  21.54  per  cent, 
a  close  approximation  to  the  longer  method. 


XXX. — ACCURACY    OF    FIRE.  *  47 

Other  Figures. 

Similar  applications  are  given  in  the  work  of  Ensign 
Glennon,  for  triangles,  trapezoids  and  rhombs,  so  that  such 
apparently  difficult  problems  as  the  probability  of  hitting 
the  gable  end  of  a  house  may  be  computed.  These  meth- 
ods are  too  elaborate  for  this  course;  but  the  following 
formula  may  be  used  for  small  arm  firing,  the  targets  in 
which  are  ellipses  whose  axes  are  determined  by  the  rela- 
tion between  the  mean  vertical  and  lateral  errors  of  the  arm 
and  ammunition. 

Ellipse: — Calling  a  and  b  the  semi-axes  of  the  ellipses 
corresponding  in  direction  to  m  and  «,  we  find  in  Glennon 


p^-2ab  fn       2a      2b          ab    \ 
\            mn   \2       3m       3?i        4=  m  n  J' 

(13) 

Circle. — If   we    make    b  =  a  —  r   the    ellipse 

becomes  a 

circle,  and 

^  _2r''  f  n        2r       2r          r^    \ 

^"^  mfi\2        3m       3n^    4.mn)  ' 

(14) 

Remarks. 

These  methods  have  a  practical  application  in  determin- 
ing the  supply  of  ammunition  necessary  to  produce  a  given 
result.  Also,  when  time  is  limited,  as  in  the  attack  of  tor- 
pedo boats,  and  the  rate  of  fire  of  the  guns  is  known,  the 
number  of  guns  to  be  mounted  on  a  certain  front  may  be 
calculated. 

In  solving  problems  for  ranges  at  which  the  mean  erroi's 
are  not  given,  these  may  be  taken  as  proportional  to  the 
squares  of  the  nearest  ranges  for  which  the  errors  are  given. 
Animate  Objects. 

The  following  table  may  be  used  in  connection  with 
problems  in  the  probability  of  small  arm  fire.  It  is  derived 
from  the  measurement  of  photographs  of  a  number  of  Ital- 
ian soldiers,  of  average  size  and  build,  taken  naked. 


48 


XXX. — ACCURACY   OF   FIRE. 


TABLE   III. 


Mean 
h't,   ft. 

Mean 

Vertical 

OBJECT. 

width, 
ft. 

Area 
sq.  ft. 

Foot  soldier,  standing,  front. 

5.3 

0.95 

5.0 

Foot  soldier,  standing,  side. 

5.3 

0.57 

3.0 

Foot  soldier,  kneeling  and  firing,  front. 

3.4 

1.00 

3.4 

Foot  soldier,  lying  down  and  firing,  front. 

1.4 

1.18 

1.7 

Foot  soldier,  lying  down  close. 

0.7 

1.64 

1.8 

Horseman  and  horse,  front. 

8.0 

1.52 

12.2 

Horseman  and  horse,  side. 

8.0 

2.4 

19.4 

Horse,  front. 

— 

— 

9.0 

Horse,  side. 

— 

— 

17.0 

IV.   MANAGEMENT  OF  FIRE. 


THE    COLLECTIVE    FIRE    OF    SMALL   ARMS. 

Advantages. 

The  need  of  reserving  fire  for  the  critical  moments  of  an 
action,  and  the  difficulty  of  controlling  the  fire  of  troops  in 
dispersed  order  have  led  to  the  use  of  collective  fire  from 
groups  of  men  under  the  direction  of  subordinate  officers. 

Careful  experiments  have  shown  that  the  superiority  of 
very  good  individual  marksmen  over  ordinary  marksmen 
diminishes  rapidly  as  the  range  increases;  while  skill  in 
collective  fire  maintains  it  superiority  at  all  ranges.  This 
skill  depends  less  upon  natural  aptitude  than  upon  practice 
under  the  disturbing  circumstances  of  collective  fire,  and 
thus  demands  "fire  discipline".  This  is  even  more  impor- 
tant for  troops  armed  with  magazine  arms  than  for  those 
armed  with  single  breech  loaders. 

Collective  fire  is  regulated  by  watching  the  dust  thrown 
up  by  the  hits,  at  least  one  half  of  which  should  fall  short. 


XXX. — ACCURACY    OF    FIRE.  49 

The  ricochet  at  low  elevations  considerably  increases  the 
efficiency  of  the  fire. 

Definitions. 

The  intersection  of  the  nucleus  and  envelope  of  the  sheaf 
of  trajectories  by  the  horizontal  plane  through  the  line  of 
sight  forms  the  beaten  zone:  the  grazed  zone  corresponds  to 
the  dangerous  space  for  the  lower  element  of  the  envelope 
and  is  taken  to  be  equal  to  that  of  the  mean  trajectory:  the 
sum  of  the  beaten  and  grazed  zones  forms  the  dangerous 
zone,  as  seen  in  figure  33. 

This  figure  represents  the  projection  of  the  sheaf  and  the 
zones  on  the  plane  of  sight.  The  line  of  sight  is  supposed 
to  coincide  with  the  surface  of  the  ground;  the  firer  lying 
down  and  aiming  at  the  enemy's  feet.  He  was  formerly 
supposed  to  stand  up  and  aim  at  the  waist. 

Constancy  of  the  Beaten  Zone. 

It  has  been  observed  that  as  the  range  increases  the  increase 
in  longitudinal  diviation  resulting  from  accidental  differences 
in  the  angles  of  departure,  is  approximately  compensated  for 
by  the  diminished  obliquity  of  the  horizontal  section  of  the 
sheaf  resulting  from  the  increased  angle  of  fall.  See  lines 
b'  z'  =  b"  z"y  figure  34.  Consequently  the  depth  of  the  beaten 
zone  is  approximately  constant  at  all  ranges,  although  the 
width  of  the  beaten  zone,  is,  except  at  extreme  ranges,  ap- 
proximately y^f,  of  the  range.  With  arms  and  ammunition 
of  the  type  of  the  service  rifle,  cal.  0.45,  it  is  about  100  yards 
for  the  nucleus,  and  about  300  yards  for  both  the  nucleus  and 
envelope,  as  shown  in  the  figure.  See  extract  from  Range 
Table,  page  52. 

Eemarks. 

These  data  are  derived  from  target  firing ;  in  battle  the 
deviations  may  be  eight  times  as  great. 


50  XXX. — ACCURACY    OV    FIRE. 

The  depth  of  the  beaten  zone  may  be  advantageously 
increased  by  varying  the  elevation  of  the  pieces  in  a  group. 
Variations  in  Dangerous  Zone.     Vulnerability. 

The  depth  of  the  dangerous  zone  varies  with; — 

1.  The  flatness  of  the  trajectory. 

2.  The  height  of  the  target. 

3.  The  range. 

4.  The  inclination  of  the  ground  to  the  line  of  sight. 

1.     FLATNESS    OF    TRAJECTORY. 

This  principally  affects  the  grazed  zone.  The  maximum 
grazed  zone  for  a  man  kneeling  is  in  round  numbers  as 
follows,  Springfield  350  yds.,  new  Hebler  550  yds.  See 
example  7;  Chapter  XX.  The  maximum  grazed  zone  is  a 
convenient  measure  of  the  power  of  the  arm  and  ammu- 
nition. Within  this  zone  adjustment  of  the  rear  sight  is 
unnecessary, 

2.    HEIGHT    OF    THE    TARGET. 

The  maximum  grazed  zone  for  a  man  standing  is,  Spring- 
field 420  yds.,  Hebler  450  yds.  In  connection  with  the 
effect  of  change  of  position  upon  the  probability  of  being 
struck  it  may  be  stated  that  at  medium  ranges  the  vulner- 
ability^ or  chance  of  being  hit  with  a  given  expenditure  of 
ammunition,  is  as  follows:  Lying  down  :  kneeling  :  stand- 
ing ::  1  ;  2  :  3.     See  ratio  of  areas  in  Table  III. 

Owing  to  the  increase  in  the  angle  of  fall  at  long  ranges 
these  differences  disappear. 

3.    RANGE.         ' 

Beyond  the  maximum  grazed  zone,  the  depth  of  the 
dangerous  zone  diminishes  as  the  range  increases;  and  so 
does  the  vulnerability,  which  is  approximately  diminished 
one  half  for  every  increase  in  range  of  250  yards. 


XXX. — ACCURACY    OF    FIRE.  51 


4.    INCLINATION  OF  THE  GROUND  TO  THE  LINE  OF  SIGHT. 

The  effect  of  variations  in  the  slope  of  the  ground  is 
shown  by  figure  34  which  represents,  but  not  to  scale, 
the  nucleus  of  a  1000  yard  trajectory. 

The  beaten  zones  B Z  dX  different  ranges  are  practically 
100  yards  in  depth,  if  measured  on  the  line  of  sight.  See 
page  49. 

The  included  figures  show  the  variations  in  the  beaten 
zone  arising  from  varying  the  inclination  of  the  ground 
respectively  -j^;  ^;  ^  above  and  below  the  line  of  sight.* 

The  limit  of  efficiency  is  reached  when  the  ground  is  par- 
allel to  the  tangent  at  and  beyond  the  object  aimed  at,  B.  In 
this  case  we  shall  have  the  largest  grazed  zone  and  a  large 
beaten  zone  making  together  a  deep  dangerous  zone.  Be- 
yond B  there  will  be  one  or  two  grazed  zones,  depending 
on,  the  height  of  the  target  T. 

For  a  given  slope  the  safe  zoiie^  x  x\  will  increase  as  the 
enemy  approaches  from  O  to  B  and  as  his  trajectory  con- 
sequently becomes  flatter.  Troops  behind  cover  will  there- 
fore be  better  protected  by  advancing  toward  the  cover  as 
the  enemy  approaches. 

This  explains  the  vulnerability  of  deep  columns  on  de- 
scending slopes  and  the  insecurity  of  apparently  good  cover  in 
rear  of  the  point  at  which  the  enemy  is  directing  his  fire. 
This  was  noticed  at  the  battle  of  Inkerman,  in  which  great 
destruction  was  wrought  among  the  horses  of  an  English 
battery  which  were  out  of  sight  of  the  enemy,  but  in  rear 

*  These  slopes  arc  found  about  West  Point  as  follows :  j 
y*^  Road  to  Post-office,  near  its  intersection  by  the  Dragoon  path. 
^^  From  S.  W.  corner  of  Academic  Building,  for  a  short  distance  to  the 

west. 
^  From  crosswalk  in  front  of  sally  port  of  Academic  Building  to  the 
north. 


52  XXX. — ACCURACY    OF    FIRE. 

of  the  guns  and  on  the  reverse  slope  of  a  hill,  the  slope  of 
the  hill  being  nearly  tangent  to  the  enemy's  trajectory. 

Effect  of  Increasing  the  Rapidity  of  Fire  of  Small  Arms. 

Owing  to  the  diminished  accuracy  of  rapid  fire,  its  effect 
in  a  given  time  increases  less  rapidly  than  does  its  rate.  It 
appears  from  experiment  that  doubling  the  rate  increases 
the  efficiency  about  IJ  times;  viz — 

Kind  of  Fire.  Kate  per  Min.  Kelative  Eflaciency 

Common  6  1.0 

Rapid  12  1.5 

Magazine  24  2.25 

The  factor  of  efficiency  may  be  determined  from  the  fol- 
lowing equation  in  which  e  is  the  factor;  n  is  the  number 
of  shots  fired  at  a  given  target  and  range,  h  is  the  number 
of  hits,  and  t  is  the  time  in  minutes  required  to  fire  the 
shots,  n. 

Then  since  the  efficiency  is  directly  proportional  to  h^  and 
inversely  proportional  to  ?t  and  to  /,  we  have 

h       h        h' 
e  =  -  x-  = ■ .  (15) 

n        i      ny^t 

Range  Table.    Extract. 

Hotchkiss  6  pdr.  R.  F.  Gun.  See  page  49.  I  V  =  1818, 
a/  =  2  lbs.,  W=  6  lbs. 


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